Journal of Modern Physics, 2013, 4, 64-76 Published Online July 2013 (
Supermassive Black Holes, the Early Universe, and
Gamma-Ray Bursts
Shawqi Al Dallal1, Walid J. Azzam2
1College of Graduate Studies and Research, Ahlia University, Bahrain
2Department of Physics, College of Science, University of Bahrain, Bahrain
Received April 18, 2013; revised May 25, 2013; accepted June 27, 2013
Copyright © 2013 Shawqi Al Dallal, Walid J. Azzam. This is an open access article distributed under the Creative Commons Attri-
bution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
Observational evidence reveals that supermassive black holes reside at the center of most galaxies up to the furthest
observable redshifts. The tight M-σ relation suggests a close operative feedback between the growth of supermassive
black holes and the growth of the galactic bulge. Models describing the formation scenarios of seeding black holes and
their growth are reviewed. In each of these models, the prevailing environments in the primordial-galactic disks, in-
cluding the gas dynamics, cooling processes, and metallic enrichment are explored. It is shown that the galactic disk
parameters set constraints on the channel of formation of the seeding black holes and their growth. Primordial black
holes from the inflationary era, their formation, possible interaction, and constraints on their observations are discussed.
Gamma-ray bursts resulting either from the collapse of massive stars, or from the collision of compact objects are ex-
plored. The abundance of these violent events in the early universe suggests a possible connection with galaxy forma-
Keywords: Black Holes; Early Universe; Gamma-Ray Bursts
1. Introduction
Astronomical observations and theoretical studies during
the past few decades have revealed the existence of black
holes with a wide spectrum of masses in the early uni-
verse [1-3]. However, current observations remain inca-
pable of directly probing the formation of supermassive
black holes, despite their importance in setting the stage
for the subsequent evolution of galaxies [4-6]. The de-
mography of black holes at the center of galaxies is an
important feature and a promising channel to enhance
our understanding of galaxy formation [7]. The Hubble
Space Telescope and the Chandra X-ray Observatory
detected supermassive black holes with masses in excess
of one billion
the origin and properties of the initial progenitor. The
logical question that might arise is to what extent modern
astronomical observatories can set the stage for probing
the evolutionary stages in galactic formation. An answer
to this question may be provided by future observatories
such as the James Webb Telescope.
In this paper we review some theoretical and observa-
tional studies of black holes in the early universe, their
origin, formation, and fate. In the first part, we outline
the observational evidence concerning the existence of
supermassive black holes in the early universe, followed
by a brief introduction to the techniques employed in the
determination of their masses. In the second part, we
present the various models for the formation of black
holes in the early universe, including the collapse of
population III stars, dynamic instabilities, collapse of gas
due dynamic instabilities, the collapse of supermassive
stars, the dynamical processes in enriched halos that lead
to the formation of massive black holes, and the forma-
tion and fate of primordial black holes. The last section
of this paper is devoted to the connection between black
holes and gamma-ray bursts.
in quasars at redshifts that corre-
spond to just few hundred million years after the Big
Bang [8,9]. The existence of supermassive black holes
imposes important constraints on their formation mecha-
nism [10]. Furthermore, the gas physics involved in their
formation is yet to be understood [5,11]. There is no de-
cisive answer concerning the formation of the earliest
black holes, primarily because their growth process masks
opyright © 2013 SciRes. JMP
2. Observational Evidence of Supermassive
Black Holes
Astronomical observations reveal that supermassive black
holes lurk at the centers of galaxies all the way up to the
furthest observable redshifts [12]. The first discovered
supermassive black hole is the one at the center of the
Milky Way Galaxy, which coincides with the location of
Sagittarius A. The Milky Way black hole has an esti-
mated mass of 4.1 million solar masses
which is relatively small when compared to the 230 mil-
black hole at the center of the Andromeda
Galaxy [14], or the 6.4 billion
supermassive black
hole lurking at the center of M87 [15,16]. The most mas-
sive supermassive black hole discovered so far has a
mass of 21 billion
and resides at the center of the
NGC 4889 galaxy in the Coma cluster [17]. Galaxy
mergers may give rise to binary supermassive black
holes as in the case of the binary system OJ287 [18]. An
interesting property of supermassive black holes is their
relatively low density, which is defined as the black
hole’s mass divided by its Schwarzschild volume. It can
easily be shown that the density of a supermassive black
hole is inversely proportional to the square of its mass,
and accordingly, since it has very high mass, its density
is usually low.
The formation of supermassive black holes in the early
universe remains one of the most controversial subjects
in astrophysics. The main issue is that our current obser-
vational tools are incapable of effectively differentiating
between the predictions of various models. Many tech-
niques have been developed to probe this issue. The
Chandra Deep Field South (CDFS), combined with very
deep optical and infrared images from the Hubble Space
Telescope gave astronomers the opportunity to look for
black holes lurking in about 200 galaxies at an era when
the universe was between 800 million to 950 million
years old [19]. The observations reveal that between 30%
and 100% of distant galaxies contain growing supermas-
sive black holes. When these results are extrapolated to
the full sky, we arrive at the huge number of about 30
million supermassive black holes in the early universe
[20,21]. One of the main objectives in studying super-
massive black holes is to understand their formation and
growth. From an observational perspective, optical tele-
scopes are not the right tool to use since they are unable
to penetrate the thick cloud of gas and dust that en-
shrouds nearly all black holes. Only high energy X-rays
can find their way through the thick veil of gas and dust
which makes the Chandra X-Ray Observatory the right
tool for achieving this task.
3. Estimation of the Mass of Supermassive
Black Holes
The determination of the masses of black holes is an es-
sential element in verifying the extent of accuracy of
various galactic formation and black hole growth models
and their adherence to observations. Two important tech-
niques are employed to estimate the masses of black
holes at the centers of galactic bulges. The first technique,
known as reverberation mapping, is the primary approach
in which the black hole mass is determined directly from
observational data, though in certain cases the estimation
of some parameters concerning gas dynamics is needed.
The second approach depends on establishing a correla-
tion between the masses of black holes and certain pa-
rameters of the hosting bulges. Both techniques will be
briefly outlined below.
3.1. Reverberation Mapping
Reverberation mapping is the primary mass estimation
technique for determining the masses of supermassive
black holes at the centers of galaxies. The technique in-
volves measuring the structure of the broad emission line
region (BLR) around a supermassive black hole, where
the mass is measured directly from the gravitationally
induced motion of the nearby gas [22]. The equation
regulating this process is given by
GM fRV
where G is the gravitational constant, ΔV is the rms ve-
locity of gas moving near the black hole as measured
from the Doppler broadening of the gaseous emission
lines, RBLR is the radius of the broad-line region, and f is a
form factor that depends on the shape of the BLR. The
measurement of RBLR is considered a serious challenge.
To perform the measurement, the adopted standard tech-
nique is based on the fact that the emission line fluxes
experience strong variation in response to changes in the
continuum, determined by the light from the accretion
disk near the black hole [23]. Moreover, these lines have
a certain delay with respect to changes in the continuum,
presumably due to the light travel time, which permits
the measurement of RBLR. Measurement of the f factor
presents an added difficulty. Simple models of BLR were
used until about 2004 to estimate f. More recently, f has
been determined by bringing the M-sigma relation for
active and quiescent galaxies into agreement [22].
3.2. The M-Sigma Relation
The correlation between the masses of supermassive
black holes and the velocity dispersion of their host bulge
was first demonstrated by Merritt [24] and Ferrarese and
Merritt [25]. This relation is used to estimate the black
holes masses in far away galaxies where no direct mass
measurement can be made, and is given by
8200 kms
Copyright © 2013 SciRes. JMP
where A is a constant of order 3, σ is the stellar velocity
dispersion of the galaxy bulge, and α is a constant of or-
der 5 representing the slope of the M-σ relation. Ferrarese
and Merritt [25] found A = 3.1 and α = 4.8 ± 0.5. To es-
tablish the above relation, the above authors assumed a
central velocity dispersion, σc, that was corrected for an
effective aperture of radius re/8, where re is the half-light
radius. Gebhardt et al. [26] used, as an independent
variable, the dispersion σe which is defined as the spa-
tially averaged rms line-of-sight stellar velocity within
the effective radius re. They found a smaller slope value:
α = 3.75 ± 0.3 and a greater vertical scatter. Merritt and
Ferrarese [27] combined the stellar gas dynamics and the
reverberation mapping mass estimates to derive a best fit
relation with A = 1.3 ± 0.36, and α = 4.72 ± 0.36. King
[28] relied on observations of intense high-speed out-
flows in quasars, and explicitly modeled the interaction
between the outflow and host galaxy without using any
free parameters and obtained an M-σ relation with A =
1.5 and α = 4. More recent studies on black hole masses
in nearby galaxies give A = 1.9 and α = 5.1. The tight
nature of the M-σ relation suggests that a feedback
mechanism is operating between the growth of super-
massive black holes and the growth of galaxy bulges.
4. Cosmological Processes in Black Hole
In this section we explore some basic processes that will
set the stage for black hole formation. Accretion around a
black hole is one of the key ingredients behind its growth.
The second essential element is the existence of a dark
matter halo that forms and grows from primordial density
fluctuations characterized by a virial radius, a mass over-
density, and a virial temperature. This halo serves as the
host for the pre-galactic disk, which usually grows via
gas dynamic processes.
4.1. Accretion around Supermassive Black Holes
Accretion around supermassive black holes is currently
considered the only mechanism capable of producing the
observed luminosities produced by supermassive black
holes in quasars [29], with a maximum efficiency of 6%
for a non-rotating black hole, and 29% for a maximally
rotating one. Therefore, matter accretion and the subse-
quent fall on a central supermassive black hole is the
main source of the tremendous amount of energy re-
leased by active galactic nuclei (AGN). If accretion is an
acceptable mechanism for black hole growth, the pro-
genitor remains controversial, with primordial black holes
[30], dark stars [31], and collapsing clouds of gas [32]
being the main candidates. Growth by the merger of stel-
lar-mass black holes was also evoked as a phase in the
formation of supermassive black holes [33]. Cold dark
matter, initially at rest, falling freely and radially onto a
central black hole would accrete without energy release
or observational effect [34]. However, an AGN exhibits a
significant amount of angular momentum precludes free
infall. The angular momentum of the accreted material
that is approaching a central black hole requires a con-
siderable loss of its angular momentum, with a typical
loss for a normal galaxy may of about 6 × 1028 cm2/s [35].
The contribution to such loss of angular momentum may
emanate from viscosity, non-axisymmetric gravitational
forces, magnetic forces, etc. [35]. For a spherically sym-
metric potential, the orbit of minimum energy for a fixed
angular momentum is a circle, and infalling accreted
material resulting from the loss of angular momentum
will take the form of successively smaller and smaller
concentric circles. Matter describing orbits inclined to
each other will eventually collide and there will be a
transfer and mixing of angular momenta of different gas
streams leading to their equalization. As a consequence,
accreted matter tends to orbit in a simple plane having a
specific angular momentum at a given radius [35].
The existence of an efficient mechanism for transport-
ing angular momentum outward will enable the accretion
material to approach a marginally stable orbit. The exis-
tence of a magnetic field in the matter flowing into the
disk, as well as turbulent motions, is one such mecha-
nism since it leads to the transfer of angular momentum
outward [36]. In accretion disks, particles lose their an-
gular momentum due to friction between adjacent layers,
and spiral toward the black hole by releasing their gravi-
tational energy. A certain amount of this energy enhances
the kinetic energy of rotation, and the rest is turned into
thermal energy irradiated from the disk surface [34].
The energy released in the accretion process and its
spectrum are primarily determined by the rate of matter
inflow onto the outer boundary of the accretion disk,
which converts matter to radiation with an efficiency η.
The Eddington accretion rate is a characteristic scale for
accretion, and is given by [34-35]
The total energy released in the disk is equal to the
Eddington luminosity
which is a critical luminosity for any given mass M, be-
yond which the radiation force overcomes gravity. Com-
bining the above two equations, we obtain for the Ed-
dington luminosity
1.51 10
L (5)
Luminosities ranging from 1042 to 1048 erg/s have been
Copyright © 2013 SciRes. JMP
observed for AGNs, corresponding to black hole masses
ranging from 105 to 109 solar masses [35]. Assuming an
accretion rate in the AGN of about 0.5 M/yr, and a ra-
diation efficiency η ~ 0.1 gives a resulting luminosity of
3 × 1045 erg/s. This luminosity corresponds to the middle
of the observed luminosity distribution of low redshift
AGN [35]. The accretion rate of the matter inflow in the
accretion disk can assume a wide range of values that
may exceed or fall short of the critical Eddington rate.
For subcritical accretion
, temperatures in
the inner region of the disk are of the order of 105 - 106 K,
corresponding to an energy release in the UV and soft
X-ray band [34]. When the accretion rate equals to or
exceeds ME, the radiation temperature increases to 107 or
108 K, and the accretion disk becomes a strong source of
X-ray radiation. For a strongly supercritical regime
, the luminosity remains fixed at the Ed-
dington critical limit LE, whereas most of the irradiated
energy from the accretion disk is in the UV and optical
region of the spectrum [34]. In the above analysis, we
have shown that a good agreement exists between obser-
vation and the theory of spectral distribution of radiation
from accretion disks of supermassive black holes. How-
ever, these theories are mainly concerned with mass ac-
cretion rates and the luminosity of the accretion disk ir-
respective of the origin of the accreting supermassive
black hole.
4.2. Primordial Dark Matter Halos
Galaxies are thought to be formed from baryonic matter
in dark matter halos born out of small primordial density
fluctuations [37]. These halos are characterized by a
virial radius rvir representing a sphere containing a mean
mass overdensity δvir [38]. There are three important pa-
rameters that can be inferred from these halos. The first
is the virial mass Mvir that can be calculated directly from
the virial theorem. The second is the circular velocity Vc
which can be calculated from the relation
vir vir
c, and the third is the virial tempera-
where mp is the proton mass, µ is the mean molecular
weight, and kB is the Boltzmann constant. The gravita-
tional collapse of the baryon component can proceed
when the mass of the overdense region reaches the Jeans
mass MJ. At masses in excess of the Jeans mass baryons
are captured and are then shock-heated by the subsequent
collapse and virialization of dark matter. A necessary
condition for star formation is that efficient cooling needs
to take place, which allows the baryonic cloud to dissi-
pate its kinetic energy and to continue its collapse and
fragmentation process [37]. The cooling process is de-
termined by how efficient an object is in dissipating en-
ergy. Gas dynamics processes predict that low-mass ob-
jects are less efficient in dissipating energy and cool
rather slowly, whereas more massive objects can cool at
a faster rate [39]. The collapsing halos in the early uni-
verse exhibit a virial temperature smaller than 104 K, and
are referred to as mini halos. At this temperature, cooling
is determined by the electron excitation of atomic hy-
drogen. A necessary condition for the gas to cool down
and form the first stars is that the halos should rely on the
less efficient H2 cooling [37].
5. Formation of Supermassive Black Holes
During the past few decades, several models have been
proposed to explain the presence of massive black holes
(MBHs) at redshifts corresponding to the era when the
universe was less than one billion years old. Important
questions to answer are when did the seeding black holes
at the centers of galaxies form, and what mechanism was
involved in their growth. Several hypotheses have been
advanced to elucidate the mechanisms leading to the
formation of supermassive black holes. It is pretty much
agreed that once a black hole resides at the center of a
galaxy, it can grow by accretion or by merging with other
black holes. The crucial issue that remains is how the
first black holes formed in the first place. The various
models we address in this work concern the seed or po-
tential progenitors of supermassive black holes observed
at the centers of galaxies. The formation of seeding black
holes at high redshifts is an essential requirement of all
models. The inferred large masses of massive black holes
(MBH) are a core element in all models explaining their
Several possible formation channels have been inves-
tigated to understand the MBH seed, including: 1) the
formation and fate of population III stars; 2) the forma-
tion mechanism resulting from gas dynamic instabilities,
including supermassive stars; 3) formation via stellar-
dynamic processes; 4) collapse of dark stars; 5) primor-
dial black holes from the inflationary era. In the follow-
ing, we shall introduce the mechanisms suggested by
various models leading to the formation of the black
holes seed, and compare the predictions of each of these
models with the latest observational findings.
5.1. Collapse of Population III Stars
Population III stars are massive metal-free objects com-
prising the first generation of stars after the Big Bang.
These stars are postulated to have formed in mini-halos
with masses of the order
and to have collapsed
from the highest primordial density field. For Tvir > 103 K,
the cooling process is mediated by molecular hydrogen
[39]. Atomic hydrogen cooling takes place in the larger
Copyright © 2013 SciRes. JMP
halos with a total mass of 8
and vir
Simulation of the collapse of molecular clouds suggests
that massive stars with
10 K
can form [40]. The
fate of population III stars depends primarily on their
masses. The collapse of 40 - 140 M low-metallicity stars
is predicted to directly form a black hole. For this range
of masses, the remaining mass is about 40% of the initial
star mass [41]. When the mass of the population III star
is in the range of 140 to 260 M, the fate of the star is
determined by the electron-positron pair production in-
stability that leads to supernovae explosions. In these
stars, central helium burning drives the core to a tem-
perature and density regime where electron-positron
pairs are created in abundance, and can convert the in-
ternal energy into rest-mass of the pair with an insignifi-
cant contribution to the pressure [42,43]. At this stage,
depending on the mass of the star, the instability causes a
rapid contraction leading either to an implosive oxygen
state or to silicon burning. In both cases the collapse is
reversed and the star is completely disrupted by a nu-
clear-power explosion. The core of the star implodes,
burns fuel, and explodes violently leaving no remnant
[44,45]. For yet higher masses
260M, the fate of
the star is determined by the photodisintegration instabil-
ity, which results from the extremely high temperature
developed at the center of the star. This process is en-
countered before explosive burning reverses the implo-
sion [43]. The energy produced in the previous burning
stage is rapidly consumed and the collapse continues its
momentum to form a black hole [43,46]. The final mass
of the born black hole may reach at least half the initial
stellar mass [45].
Supernovae predicted by this model for certain ranges
of massive stars will release a colossal amount of energy
that can be detected by current observatories. No such
events have been recorded so far. On the other hand, the
above model has large uncertainties concerning the final
mass of the population III stars. Among these uncertain-
ties is whether a single star or multiple stars are formed
per halo. In fact, the initial mass function itself is not
well known. For this issue, and other related matters, the
reader may consult the following references [47-49].
5.2. Gas-Dynamic Instabilities
Metal-free or metal-poor proto-galaxies are efficient nurs-
eries where black holes can be formed and grow. In these
systems, supermassive black holes can also be formed
directly out of a dense gas cloud [50-52]. On the other
hand, enriched halos exhibit an efficient cooling process
which favors fragmentation and star formation rather
than direct black hole formation. In metal-free gas clouds
that characterize the very first proto-galaxies, the col-
lapse is expected to occur only in massive halos with
virial temperatures vir, where the formation of
molecular hydrogen is inhibited [53]. At these tempera-
tures H2 formation is inhibited and atomic hydrogen be-
comes an efficient agent for cooling down the tenuous
gas until it reaches 4000 K [37]. The same process is
encountered for slightly enriched gas below the threshold
of fragmentation. Suppression of H2 formation requires
critical UV fluxes that are much more important than the
cosmic UV background. Fragmentation occurs when the
gas is enriched above a critical metallicity [54]. At
vir, the line-trapping of Lyman-α photons in
isothermally collapsing gas causes the equation of state
to stiffen with the consequence that fragmentation be-
comes harder to achieve provided that the metallicity
does not exceed about 104 of the solar metallicity [54].
The dissociation of H2 in these systems is brought about
by Lyman-α trapping. In such halos, gas cooling and
contraction proceed gradually with no fragmentation until
rotational support halts the collapse, which usually oc-
curs before reaching densities that allow the formation of
a massive black hole (MBH). Analysis of the rotational
dynamics of the collapsing gas shows that tidally induced
angular momentum can provide centrifugal support that
halts the collapse only at a distance of about 20 pc [37],
and ultimately leads to the formation of a disk. Forma-
tion of an MBH requires the additional transfer of angu-
lar momentum to foster the gas collapse process. Many
models have been proposed to provide the additional
transfer of angular momentum, leading to the formation
of MBH. An efficient mechanism to achieve this transfer
was proposed by Shlosman et al. [55] and Begelman et al.
[56]. In these models, efficient angular momentum trans-
fer is achieved by dynamical instabilities. These authors
proposed the so called “bars-within-bar” mechanism,
which originates from the global gravitational instability
and dynamical infall. Thus, self-gravitating gas clouds
become bar-unstable when the level of rotational support
exceeds a certain threshold. A bar is a channel for the
outward transportation of angular momentum via gravi-
tational and hydrodynamical torques, which will cause
the radius to shrink. Gas cooling and gas shrinking fur-
ther enhance the instability and cause the process to cas-
cade. This mechanism is successful in accumulating gas
at the center of the halos.
10 KT
10 KT
Local, rather than global, instabilities in a self-gravi-
tating galactic disk can be calculated using the Toomre
stability parameter formalism. The Toomre parameter Q
is defined as
where Σ is the surface mass density, cs is the speed of
sound, and 2VR
is the epicyclical frequency,
and V is the circular velocity of the disk. Gravitational
Copyright © 2013 SciRes. JMP
instabilities occur when Q approaches a critical value Qc.
Instabilities might lead to mass infall rather than frag-
mentation and star formation, provided that destabiliza-
tion of the system is kept below a threshold value. This
happens when the inflow rate is below a critical threshold
where αc is the viscosity parameter. This process contin-
ues until the mass accumulated at the center (Ma) is
enough to make the disk marginally stable. The mass is
computed from the Toomre instability criteria by requir-
ing that Q = Qc, and assuming a DM halo mass that is
determined from 23
vir h
TM [57]
MfM (9)
8fQf jT T
max vir ga
dcd d. Here, max
is the maximum halo spin parameter, fd is the gas fraction
participating in the infall, jd is the fraction of the halo’s
angular momentum retained by the collapsing gas. The
upper limit of the mass that can contribute to MBH for-
mation is determined by the mass and spin parameter of
the halo.
5.3. Collapse of Supermassive Stars
Gas dynamical processes can also lead to the formation
of supermassive stars (SMS) that may collapse, under
certain conditions, to form a MBH. Gas accumulated at
the few parsecs around the center of the halo by proc-
esses described in the previous section, can reach 104 to
106 M. For efficient gas accumulation, a SMS
may form, which eventually collapses
to form a black hole [37]. SMS of a given mass, and
supported by radiation pressure, will evolve as an
polytrope [58,59]. It has been shown that the rotation of
SMS in a post-Newtonian approximation cannot halt the
collapse, and thus an MBH is likely to form [59]. Shibata
and Shapiro [60] considered marginally instable and maxi-
mally rotating SMS using general relativity and found
that the star will form a Kerr-like black hole containing
90% of the stellar mass.
In systems where mass accumulation is fast enough,
the outer layers of the SMS are not thermally relaxed
during much of the lifetime of a main sequence star [61].
These stars exhibit complex structures with a convective
core surrounded by a convectively stable envelope con-
taining most of the star’s mass. Hydrogen burning in the
core of these stars is relatively low, and continues
throughout most of its massive stages. When hydrogen is
exhausted, the SMS will contract and suffer catastrophic
neutrino losses that lead to its collapse to an initial black
hole with a mass of a few
of a low-mass central black hole surrounded by a mas-
sive radiation-pressure-supported envelope. The black
hole grows gradually at the expense of the massive en-
velope until the resulting MBH is unveiled. The rate of
mass transfer supplied to the black hole’s sphere of in-
sup is determined by the Bondi rate evalu-
ated at the black hole’s radius of influence. This process
is usually suppressed due to the back reaction of the en-
ergy flux inside the radius of influence [63]. The accre-
tion rate is thus reduced to [64,65]
, that grows subsequently
via accretion from the resulting bloated envelope. This
object is referred to as quasistar [56,62], and it consists
supBH s
The above relation assumes an absence of a wind that
modifies the energy and/or momentum. The quasistar
expands gradually and the black hole accretion rate is
such that the feedback energy flux equals the Eddington
limit. If the feedback average flux exceeds the Eddington
limit, the black hole grows at a super-Eddington rate and
the photospheric temperature decreases until it reaches a
minimum value of about , below which no
hydrostatic solution for the convective envelope exists.
At this point, the convective zone releases energy at a
super-Eddington rate and the final limit of the black hole
seed mass is set. The range of masses of the seed is 104
to 105 M, depending on the model.
5.4. Dynamical Processes in Enriched Halos
Star formation can proceed in mini-halos characterized
by a virial temperature Tvir < 104 K [40,66]. The halos
will be enriched with metals by the first generation of
population III stars, and thus fragmentation and forma-
tion of low mass stars will be a natural outcome of this
enrichment [67]. This process sets the stage for new ho-
rizons of MBH formation. Stellar dynamical processes
may lead to the formation of compact star clusters [29,
68], resulting from collisions. These collisions arise from
dynamical interactions and may play a major role in the
formation of very massive stars (VMS) leading to the
formation of MBH remnants in the range 102 - 104 M
[69]. In an attempt to reach equilibrium, the compact
core cluster initially contracts and then starts to decouple
thermally from its outer region. Energy transfer from the
central dense core will cause a rapid core collapse [70].
Dynamical friction causes a segregation of more massive
stars in the center. If these massive stars remain in the
main sequence stage, then a subsystem will be developed
and will decouple from the cluster. In this subsystem, star
collisions can proceed in a runaway manner eventually
leading to the growth of VMSs [71]. The fate of VMSs
depends essentially on their metal enrichment. Metal
enriched VMSs will lose much of their mass and end
their life as less massive objects (~150 M) [72]. The
final fate is either a low-mass black hole or a pair-insta-
Copyright © 2013 SciRes. JMP
bility supernova. For low metallicity, VMSs may have a
different fate. Stars with masses 40 M and sub-solar
metallicity may collapse directly into a black hole with-
out a supernova explosion. At a certain level of metallic-
ity, stars start forming in the entire proto-galactic disk. A
fraction of about 0.05 of proto-galaxies at z ~ 10 - 20,
form black hole seeds of masses ~1000 - 2000 M [69].
5.5. Dark Stars in the Early Universe
Dark stars are a new line of research that proposes that
the first stars in the universe were fueled by dark matter
heating rather than by nuclear fusion [73]. Weakly inter-
acting massive particles (WIMPs) are considered among
the best dark matter candidates [74]. It is assumed that in
the early universe the density of dark matter was suffi-
ciently high to trigger dark matter annihilation [75]. The
annihilation products of WIMPs inside a star can be
trapped to produce enough energy to heat its core and
prevent its collapse. The first stars are postulated to form
inside dark matter halos of masses of the order of 106 M
[76], with one single star per halo. It is also argued that
these stars set the stage for many important processes
like reionization, the seeding of supermassive black holes,
and the production of heavy elements in subsequent gen-
erations of stars. The lightest neutralino is motivated by
supersymmetry (SUSY) arguments and is considered the
best WIMP candidate in the Minimal Supersymmetric
Standard Model [77]. The rate of energy production per
unit volume resulting from WIMP annihilation is [76]
x x
 
ann (11)
where 26 3
310 cmsec
100 GeVm
ann is the annihilation
cross-section of weak interaction, and x is
the WIMP mass. Three key criteria were postulated for
dark stars, namely: 1) high dark matter densities; 2) a
clumping of annihilation products inside the star; and 3)
DM heating overcoming other heating mechanisms. The
first criterion is revealed from the above equation, where
DM annihilation rate scales as the WIMP density squared
. Dark matter densities in the early universe are
assumed to be higher by a factor of [76]. As the
protostar forms at the center of the halo, further en-
hancement occurs resulting from the deepening of the
potential well at the center [73]. The second criterion
assumes a substantial fraction fQ of the annihilation en-
ergy is dissipated in the gas and causes its heating up at a
rate of fQ Qann per unit volume. Electrons and positrons
can deposit energy in the core, whereas neutrinos escape
far from the cloud. For the third criterion, it is assumed
that a critical transition takes place when the gas density
reaches . Above this density, DM heating
dominates over all relevant cooling mechanisms, par-
ticularly H2 cooling [78]. The first stars that formed this
10 cmn
way have MDS = 800 M [76]. When DM annihilation
inside the dark star fades out, it contracts until the tem-
perature reaches 108 K and fusion sets in. A possible end
result is the formation of a supermassive black hole, such
as those that have been found at high redshifts,
with a mass of 109 M.
In the dark star model, authors assumed a mass of 100
GeV for the annihilating WIMPS. So far, WIMPs in
general and neutralinos in particular have not been de-
tected despite intensive searches during the past few
decades. Furthermore, no trace of supersymmetric parti-
cles has been found in the Large Hadron Collider (LHC),
even though it attains energies of seven tera-electron
volts, which is far in excess of the 100 GeV postulated
for annihilating DM particles in dark stars. Also, it is
assumed in the dark star model that annihilating particles
are the source of heat or thermal radiation. All observa-
tions so far confirm that DM interacts with normal matter
only gravitationally, resulting in lensing effects of fara-
way background galaxies. Theoretical work [79] suggests
that the interaction of DM with baryonic matter is of a
gravitational nature only with no electromagnetic com-
ponent. A recent review of DM [80] indicates that its
origin may defy conventional ideas and belongs to the
realm of extra-dimensions postulated by superstring theo-
ries. In short, the DM model in its present form is inca-
pable of addressing some fundamental issues about the
origin of DM and its presumed interaction with baryonic
5.6. Primordial Black Holes
Theoretical studies of the possibility of formation of
primordial black holes (PBH) in the early universe date
back to the original work of Hawking [1]. He argued that
extreme densities and inhomogenities in the early uni-
verse can lead to the local collapse of matter resulting in
the formation of black holes. More recently, Choptuik
[81] and Kim [82] demonstrated the formation of PBHs
in the inflationary era, during which the energy density
of the universe experienced a dramatic decrease leading
to a cosmological phase transition. Hawking [1] argues
that PBHs formed in a wide spectrum of masses in the
early universe ranging from 105 g, corresponding to the
Planck mass, to 1017 solar masses. His upper limit for
mass exceeds, by many orders of magnitude, even the
greatest masses of supermassive black holes observed
today in galactic centers. On the other hand, the forma-
tion of very small black holes may arise either from the
softening of the equation of state [83], phase transitions
[84], or from the collapse of hypothetical cosmic strings
Overdense regions in the early universe may collapse
to a black hole if the gravitational attraction overcomes
Copyright © 2013 SciRes. JMP
the pressure forces and the velocity of expansion [74].
This condition is fulfilled when the potential energy for
exceeds the kinetic energy of expansion
where R is the radius of a region in the early universe,
is the energy density. The units are such that
. In a Friedman universe the sum of
these energies is zero. Therefore
1Gc 0k
Furthermore, Hawking assumed that the equation of
state relating the pressure P and the energy density
has the form 3P
, and that
is proportional to
. Thus,
nd ~tRt
A necessary condition for the collapse to occur is that
the gravitational energy,
, should exceed the internal
energy . Taking
and U, the con-
dition for collapse to occur becomes
for log
, and 3log
, the con-
dition for collapse reduces to
Once a black hole is formed, it will grow by accreting
nearby matter. The rate of accretion was calculated by
Zeldovitch and Navikov [86]
t (18)
here is the density of the background universe.
But since (see above), hence
M (19)
where o
is the initial mass of the black hole and ois
the time of formation. Thus, if o
is small compared to
o, that is, if the black hole is small compared to the par-
ticle horizon, then o
Mremains small and there
would be almost no accretion. However, if o
is of the
same order as t, then the Zeldovitch-Navikov argu-
ment leads to
t. In this case, the accretion would
cause the black hole to grow at the same rate as the parti-
cle horizon, producing black holes of the order of the
Hubble radius if the growth continued to the present time,
or it would reach a mass of 1015 to 1017 solar masses if
the growth was at the same rate as that of the particle
Carr and Rees [85] demonstrated that the density fluc-
tuations of a Gaussian distribution lead to a probability
that a given region evolves into a black hole given by
exp 2P
 (20)
is a constant defined by the equation of state where
, and
is a constant. A black hole is unlikely
to form for
of the order of 1 and for
much less
than 0.1. Lin et al. [86] demonstrated that the Einstein
equation for a stiff equation of state
permits a
spherically symmetric solution in which pressure gradi-
ents cause a black hole to grow as fast as the universe. It
was argued that only hot models of the early universe are
capable of producing PBHs prolifically enough to be
consistent with observations. Harada [87] considered the
growth of super-horizon PBHs, assuming a mass scale
hf f
which is contained in the Hubble hori-
zon of the formation epoch. Here, G, c and tf are, respec-
tively, the gravitational constant, the speed of light, and
the formation time from the Big Bang. A typical mass
scale of PBHs corresponds to the horizon mass scale of
the formation epoch
,, 100 MeV
PBHfh f
ct T
and the mass accretion rate for a black hole was esti-
mated as
 (22)
where A
is the accretion radius,
is the
speed of sound,
is the density at infinity, and
a constant of order unity. Harada [87] assumed that
given by the density of the background Friedman uni-
verse, and
is of the order of the speed of light. In
this case, the accretion rate can be integrated to give
where is a constant, and
is the mass
of the PBH at the formation time
trelative to the Big
Bang. Harada [87] obtained three categories of solutions,
namely: sub-horizon, self-similar, and super-similar. In
his paper, the effect of cosmological expansion was ne-
glected, since it is important only for the cosmological
horizon scale. The above analysis is expected to be valid
only for PBHs much smaller than the cosmological hori-
zon scale.
Copyright © 2013 SciRes. JMP
5.7. Hawking Evaporation of Black Holes
Quantum gravitation effects are usually neglected when
calculating the formation and evaporation of black holes.
The justification for this approach is that the radius of
curvature of spacetime outside the event horizon is very
large compared to the Planck length
10 cm
Gc, which is the length scale on
which quantum fluctuations of the metric are expected to
be of the order of unity [88]. Hawking derived an ex-
pression for the emission spectrum that mimics a Planck
radiation law using the usual quantum mechanical wave
equation for a collapsing object with a post collapse clas-
sical wave metric. He showed that quantum mechanical
effects cause black holes to create and emit particles as if
they were blackbodies of temperature
0 K
10 gM
10 gM
Thus, the Hawking temperature is inversely propor-
tional to the black hole mass M. Therefore, as the black
hole radiates, its temperature increases. The evaporation
of black holes was a source of controversy for some time.
To solve this dilemma, detection of PBHs was the sub-
ject of intense research since their existence was postu-
lated in the early 1970s. Hawking [88] and Page [89]
have shown that in order for PBH evaporation to occur in
our current epoch, they must have a mass .
The evaporation is accompanied by a burst of high en-
ergy particles and gamma rays [90]. The clustering of
PBHs was considered by Page and Hawking [90]. They
found that for , the maximum allowed space
density of PBHs is
11 3
10 Cpc
15 g
, where C is the
clumping factor. Cline [91] relied on data obtained from
the EGRET detector aboard the Compton Gamma Ray
Observatory to attribute some of the observed gamma-
ray flux to the evaporation of PBHs, which is strongly
clustered in the galactic halo. Furthermore, he argued
that the galactic gamma-ray halo arises primarily from
the evaporation of PBHs. Accepting the data at face
value implies that the existence of PBHs no longer re-
sides in the realm of theoretical speculation. Several con-
straints limit the mass range of primordial black holes
that can be observed. As mentioned above, black holes
with an initial mass smaller than are ex-
pected to be already evaporated. A constraint is set for
more massive black holes as determined by microlensing
techniques [92] and from spectral distortions of the cos-
mic background radiation [93].
6. The Connection between Black Holes and
Gamma-Ray Bursts
Gamma-ray bursts (GRBs) are the most powerful explo-
sions in the universe, and hold great promise as cosmo-
logical probes of the early universe. They were seren-
dipitously discovered in the late 1960s [94], and although
a great deal of effort has gone into understanding these
enigmatic explosions, the precise physical mechanism
behind their formation remains elusive. Traditionally,
GRBs have been classified, based on duration, into long
bursts (LGRBs) with T90 > 2 s, and short bursts (SGRBs)
with T90 < 2 s, where T90 is the duration needed to accu-
mulate 90% of the burst’s fluence [95]. However, some
recent studies have provided evidence for a third class of
GRBs called Very Short Gamma-Ray Bursts (VSGRBs)
with a T90 < 0.1 s [96]. For some recent reviews on GRBs,
the reader is referred to [97-102]. In this section, we will
explore the connection between black holes and all three
classes of GRBs.
According to current theoretical models, the formation
of GRBs is intimately related to black holes regardless of
whether we are dealing with long, short, or even very
short bursts. We shall start off by investigating this con-
nection for LGRBs and SGRBs, and then consider
VSGRBs where the mechanism is somewhat different.
The leading progenitor model for the formation of
LGRBs is the so-called collapsor model. In this model,
the rotating core of a massive star collapses, and the re-
leased energy is channeled out in the form of relativistic
beams [103,104]. According to this model, the minimum
angular momentum needed is basically the value associ-
ated with the last stable orbit around a black hole which,
for a non-rotating black hole, is given by [102]:
12 16 2
JGMc MM
and for a rotating black hole with a Kerr parameter a = 1,
it is given by [9]:
12 16 2
JGMcM M
where G is the universal gravitational constant, c is the
speed of light in vacuum, MBH is the mass of the black
hole, and
Two conditions that should be kept in mind concern-
ing the collapsor model are that in order for this model to
work the jets must be able to pierce through the star and
escape, and the star should not explode prematurely, oth-
erwise a black hole will not form [102]. Recent investi-
gations indicate that the Blandford-Znajek mechanism
[105] is probably behind the formation of the relativistic
jets, and these energy-loaded jets, when injected near the
center of a massive star, are able to penetrate the star and
form a streaming jet with the necessary opening angle
and Lorentz factor [102].
is the mass of the sun.
The progenitors of SGRBs are currently believed to be
mergers of compact stars: two neutron stars or a neutron
star and a black hole. Either scenario is expected to lead
Copyright © 2013 SciRes. JMP
to the formation of a black hole that is surrounded by a
torus of debris [106]. Since there is no external feeding
of the accretion disk, then the event is not expected to
last too long—on the order of one second. The two main
sources of energy that act as a reservoir for the SGRB are
the binding energy of the material that is orbiting in the
disk, and the black hole’s spin energy. In fact, it has been
estimated that up to 29% of the black hole’s rest-mass
energy and about 42% of the rest-mass found in the disk
can be extracted and utilized to power the SGRBs [106].
If dM/dt is the mass inflow rate, then to support the
SGRB, it must be at least [106]:
Mt eL
gs sM
where LSGRB is the luminosity of the SGRB and
is t
lso intimately involved in the produc-
in this section, it seem
7. Conclusion
various scenarios for the formation o
[1] S. W. Hawki the Royal Astro-
. 30-31.
overall efficiency.
Black holes are a
n of VSGRBs. According to [96], VSGRBs constitute
a separate class of GRBs for several observational rea-
sons. First, VSGRBs show considerable anisotropy in
their galactic angular distribution, and their V/Vmax dis-
tribution also points to a “local” distance scale. Further-
more, only a small percentage (about 25%) have ob-
served afterglows, compared to about 78% for SGRBs.
VSGRBs can be produced by primordial black hole
BHs). A supporting piece of evidence is that the rising
part of the time profiles of VSGRBs is in good agree-
ment with PBH evaporation models [3]. The extremely
high temperatures and pressures that existed right after
the Big Bang were conducive to the production of PBHs.
Fluctuations in the density of matter could have produced
PBHs that persisted to our present time [107-109]. Ac-
cording to [107], PBHs with masses less than about 5 ×
1011 kg would have evaporated by now. These evaporat-
ing PBHs can be detected through their Hawking radia-
tion, and may appear as very short bursts as modeled in
[110], with time durations of the order of 0.1 s and with a
luminosity of about 1033 erg/s.
From what has been stated s no
asonable to conclude that black holes are intimately
involved in the production of all three classes of GRBs:
long, short, and very short bursts.
In this paper, the f
seed black holes in the early universe and their subse-
quent growth to supermassive black holes were presented.
The M-σ relation suggests a common root for black holes
and active galactic nuclei. Cosmological processes in-
volving the seeding primordial dark halos and the pre-
galactic accretion disks were introduced in order to shed
light on the subsequent paths for the formation of galax-
ies. The various channels leading to the formation of
supermassive black holes were discussed as well. Metal-
lic enrichment and virial temperatures were found to play
a major role in determining the behavior of gas dynamics
in pre-galactic discs, and thus in the subsequent forma-
tion of the seeding black holes. Metal-free or metal-poor
environments favor the formation of population III stars
that end their lives as massive black holes. In this envi-
ronment, black holes can also be formed directly out of a
dense gas cloud. In metal rich environments, fragmenta-
tion and star formation is the dominant mechanism.
Black holes are formed in these systems by the collision
of stars in clusters and the subsequent sinking to the cen-
ter of the pre-galactic disk. Gas dynamical processes can
also lead to the formation of supermassive stars that end
their lives as massive black holes. Dark stars, as a possi-
ble channel leading to the formation of massive black
holes, were also discussed. No observational evidence
has been found so far for the existence of supersymmet-
ric particles, which are presumed to be responsible for
producing the necessary heat at the core of dark stars,
despite the fact that energies well above that postulated
for their existence have been probed. The formation of
primordial black holes from the inflationary era was also
reviewed. Theoretical studies show that these objects
were formed with a wide spectrum of masses. However,
it should be kept in mind that distortion signatures in the
microwave background radiation set a limit on the
masses of primordial black holes. Hawking evaporation
is a key element in exploring the validity of primordial
black hole models. Recent observations are in favor of
their existence. Furthermore, we discussed the important
connection between the powerful stellar explosions known
as gamma-ray bursts and black holes, and how under-
standing one of them may lead to a better understanding
of the other.
ng, Monthly Notices of
mical Society, Vol. 152, 1971, p. 75.
[2] S. W. Hawking, Nature, Vol. 248, 1974, pp
[3] B. J. Carr, Astrophysical Journal, Vol. 205, 1975, p. 1.
[4] J. Silk and M. J. Rees, Astronomy & Astrophysics, Vol.
oeb, Physics Reports, Vol. 349,
331, 1998, pp. L1-L4.
[5] R. Barakana and A. L
2001, pp. 125-238. doi:10.1016/S0370-1573(01)00019-9
[6] M. Volonteri, F. Haardt and Madau, Astrophysical Jour-
nal, Vol. 582, 2003, pp. 559-573. doi:10.1086/344675
[7] S. Tremaine, et al., Astrophysical Journal, Vol. 574, 2002,
pp. 740-753.
[8] A. J. Barth, et al., Astrophysical Journal Letters, Vol. 594,
2003, pp. L95-L98.
Copyright © 2013 SciRes. JMP
[9] C. J. Willott, et al., Astronomical Journal, Vol. 134, 2007,
pp. 2435-2450. doi:10.1086/522962
. 52-61.doi:10.1086/174548
[10] Z. Haimian, Astronomical Journal, Vol. 613, 2004, pp.
[11] A. Loeb and F. A. Rasio, Astrophysical Journal, Vol. 432,
1994, pp
[12] X. Fan, et al., Astronomical Journal, Vol. 121, 2001, pp.
54-65. doi:10.1086/318033
[13] A. M. Ghez, et al., Astronomical Journal, Vol. 620, 2005,
pp. 744-754.
[14] R. Bender, et al., Astronomical Journal, Vol. 631, 2005,
pp. 280-300. doi:10.1086/432434
[15] F. Macchetto, et al., Astronomical Journal, Vol. 489,
1997, p. 579.
[16] K. Gebhardt and J. Thomas, Astronomical Journal, Vol.
700, 2009, pp. 1
[17] N. J. McConnell, Nature, Vol. 480, 2011, pp. 215-218.
[18] M. J. Valtonen, et al., Nature, Vol. 452, 2008, pp. 851
[19] E. Treister, et al., Nature, Vol. 474, 2011, pp. 356-358.
doi: 10.1038/nature10103. doi:10.1038/nature10103
[20] L. L. Cowie, A. J. Barger and G. Hasinger, Astronomica
Journal, Vol. 748, 2012, p. 50.
[21] C. Willott, Astronomical Journal
, Vol. 742, 2011, pp.
o and S. Ca-
V. Charmandaris, Dynamics
[22] D. Merritt, “Dynamics and Evolution of Galactic Nuclei,”
Princeton University Press, Princeton, 2
[23] B. M. Peterson and K. Horne, “Reverberation on Map-
ping of Active Galactic Nuclei,” In: M. Livi
sertano, Planets to Cosmology: Essential Science in the
Final Years of the Hubble Space Telescope, Proceedings
of the Space Telescope Science Institute Symposium,
Baltimore, 3-6 May 2004, Cambridge University Press,
Cambridge, Space Telescope Science Institute Sympo-
sium Series, Vol. 18, 2006.
[24] D. Merritt, “Black Holes and Galaxy Evolution,” In F.
Combes, G. A., Mamon and
of Galaxies: From the Early Universe to the Present, As-
tronomical Society of the Pacific, 1999, pp. 221-232.
[25] F. Ferrarese and D. Merritt, Astronomical Journal, Vol.
539, 2000, pp. L9-L12. doi:10.1086/312838
[26] K. Gebhardt et al., Astronomical Journal, Vol. 539, 2000,
pp. L13-L16.
[27] D. Merritt and F. Ferrarese, Astronomical Journal, Vol.
547, 2001, pp. 140-145. doi:10.1086/318372
[28] A. King, Astronomical Journal, Vol. 596, 2003, pp. L27-
L29. doi:10.1086/379143
[29] P. Schneider, “Extragalactic Astronomy and Cosmology:
An Introduction,” Springer-Verlag, Heidenberg, 2006.
[30] A. Barrau, Astroparticle Physics, Vol. 12, 2000, pp. 269-
275. doi:10.1016/S0927-6505(99)00103-6
[31] K. Freese, P. Gondolo and D. Spolyar, “The Effect of
Dark Matter on the First Stars: A New Phase of Stellar
yal Astronomical Society, Vol.
p. 337-355.
In: A. D. Wacher and R. J.
Evolution,” Proceedings of First Stars III, Santa Fe, 16-
20 July 2008, pp. 42-44.
[32] S. M. Koushiappas, J. S. B. Bullock and A. Dekel,
Monthly Notices of the Ro
354, pp. 292-304.
[33] M. C. Miller and V. M. Lauburg, Astrophysical Journal,
Vol. 692, 2009, p. 91
[34] N. I. Shakura and R. A. Sunyaev, Astronomy and Astro-
physics, Vol. 24, 1973, p
[35] J. H. Krolik, “Active Galactic Nuclei,” Princeton Univer-
sity Press, Princeton, 1999.
[36] P. Jovanovic and L. C. Popovoc, “X-Ray Emission from
Accretion Disks of AGN,”
Propst, Eds., Black Holes and Galaxy Formation, Nova
Science Publishers, Inc., Hauppauge, 2010.
[37] M. Volonteri, The Astronomy and Astrophysics Review,
Vol. 18, 2010, pp. 279-315.
[38] V. R. Eke, S. Cole and C. S
the Royal Astronomical Society, V
. Frenk, Monthly Notices of
ol. 282, 1996, pp. 263-
280. doi:10.1093/mnras/282.1.263
[39] M. Tegmark, et al., The Astrophysical Journal, Vol. 474,
1997, p. 1.
[40] V. Bromm, P. S. Coppi and R. B. Larson, The Astro-
physical Journal Letters, Vol. 527, 1999, pp. L5-L8.
[41] W. Zhang, S. E. Woosley and A. Heger, The Ast
physical Journal, Vol
. 679, 2008, pp. 639-654.
[42] Z. Barkat, G. Rakavy and N. Sack, Physical Re
ters, Vol. 18, 1967, p
view Let-
p. 379-381.
[43] J. R. Bond, W. D. Arnett and B. J. Carr, The Astrophysi-
cal Journal, Vol. 280, 1984, pp. 82
[44] R. P. Kudritzki and J. Puls, Annual Review of Astronomy
and Astrophysics, Vol. 38, 2000, pp. 613-66
[45] C. L. Fryer, S. E. Woosley and A. Heger, The Astro-
physical Journal, Vol. 550, 2001, pp. 372-382.
[46] S. E Woosley and T. A. Weaver, Annual Revie
tronomy and Astroph
w of As-
ysics, Vol. 24, pp. 205-253.
[47] S. C. O. Glover, et al., IAU Symposium, Vol. 255
pp. 3-17.
, 2008,
01-605. doi:10.1126/science.1173540
[48] M. J. Turk, T. Abel and B. O’Shea, Science, Vol. 325,
2009, pp. 6
[49] M. Trenti, et al., The Astrophysical Journal, Vol. 700,
2009, pp. 1672-1679. doi:10.1088/0004-637X/700
[50] M. G. Haehnelt and M. J. Rees, Monthly Notices of the
Royal Astronomical Society, Vol. 263, 1993, pp.168-178.
[51] A. Loeb and F. A. Rasio, The Astrophysical Journal, Vol.
432, 1994, pp. 52-61. doi:10.1086/174548
[52] G. Lodato and P. Natarajan, Monthly Notices of the Royal
Astronomical Society, Vol. 371, 2006, pp. 1813-1823.
[53] V. Bromm and A. Loeb, The Astrophysical Journal, Vol.
Copyright © 2013 SciRes. JMP
596, 2003, pp. 34-46. doi:10.1086/377529
[54] F. Santoro and J. M. Shull, The Astrophysical Journal,
Vol. 643, 2006, pp. 26-37. doi:10.1086/501518
[55] I. Shlosman, J. Frank and M. C. Begelman, Nature, Vol.
338, 1989, pp. 45-47. doi:10.1038/338045a0
[56] M. C. Begelman, M. Volonteri and M. J. Rees, Monthly
Notices of the Royal Astronomical Society, Vol. 370,
al Society, Vol. 295, 1998, pp. 319-
2006, pp. 289-298.
[57] H. J. Mo, S. Mao and S. D. M. White, Monthly Notices of
the Royal Astronomic
336. doi:10.1046/j.1365-8711.1998.01227.x
[58] T. W. Baumgate and S. L. Shapiro, The Astrophysical
Journal, Vol. 526, 1999, pp. 941-952.
[59] M. Saijo, et al., The Astrophysical Jo
2002, pp. 349-361.
urnal, Vol. 569
[60] M. Shibata and S. L. Shapiro, Astrophysical Journal Let-
ters, Vol. 572, 2002, pp. L39-L43. doi:10.1
Vol. 387,
[61] M. C. Begelman, Monthly Notices of the Royal Astro-
nomical Society, Vol. 402, 2009, pp. 673-681.
[62] M. C. Begelman, E. M. Rossi and P. J. Armitage, Monthly
Notices of the Royal Astronomical Society,
2008, pp. 1649-1659.
[63] A. V. Gruzinov, The A
1998, p. 787.
strophysical Journal, Vol. 501,
[64] R. D. Blandford and M. C. Begelman, Monthly Notices of
the Royal Astronomical Society, Vol. 303, 1999, pp. L1-
L5. doi:10.1046/j.1365-8711.1999.02358.x
[65] R. D. Blandford and M. C. Begelman, Monthly Notices of
the Royal Astronomical Society, Vol. 349, 2004, pp. 68-
86. doi:10.1111/j.1365-2966.2004.07425.x
[66] T. Abel, G. L. Bryan and M. L. Norman, The Astrophysi-
cal Journal, Vol. 540, 2000, pp. 39-44.
[67] K. Omukai, R. Schneider and Z. Haim
physical Journal, Vol
an, The Astro-
. 686, 2008, pp. 801-814.
[68] P. C. Clark, S. C. O. Glover and R. S. Klessen,
trophysical Journal, V
The As-
ol. 672, 2008, pp. 757-764.
[69] B. Devecchi and M. Volonteri, The Astrophysical Jo
Vol. 694, 2009, pp. 3
[70] L. Spitzer, “Dynamical Evolut
Princeton University Press, Princeto
ion of Globular Clusters,”
n, 1987.
, 2009, pp. 105-126.
: 051101.
[71] Z. S. F. Portegies, et al., Astrophysics, Vol. 348, 1999, pp.
[72] E. Gaburov, J. Lombardi and Z. S. Portegies, Astrophys-
ics, Vol. 402
[73] D. Spolyar, K. Freese and P. Gondolo, Physical Review
Letters, Vol. 100, 2008, Article ID
[74] J. L. Feng, Annual Review of Astronomy and Astrophysics,
Vol. 48, 2010, pp. 495-545.
[75] L. Krauss, et al., The Astrophysical Journal, Vol. 299,
1985, pp. 1001-1006. doi:10.1
rs in the Uni-
[76] K. Freese, et al., “Dark Stars: The First Sta
verse may be Powered by Dark Matter Heating,” 2008.
[77] J. Primack, D. Seckel and B. Sadoulet, Annual Review of
Nuclear and Particle Science, Vol. 38, 1988, pp. 751-807
[78] D. Hollenbach and C. F. McKee, Astrophysical Journal
Supplement Series, Vol. 41, 1979, pp. 555-592.
[79] L. S. Schlman, Physical Review Letters, Vol. 83, 1999, pp.
5419-5422. doi:10.1103/PhysRevLett.83.5419
[80] S. Al Dallal and W. J. Azzam, Journal of Modern Physics,
Vol. 3, 2012, pp. 1131-1141.
[81] M. W. Choptuik, Physical Review Letters, Vol. 70, 1993,
pp. 9-12. doi:10.1103/PhysRevLett.70.9
Vol. 62, 2000, Article ID: [82] H. I. Kim, Physical Review D,
063504. doi:10.1103/PhysRevD.62.063504
[83] V. Canuto, Monthly Notices of the Royal Astronomical
art, Physical
Society, Vol. 184, 1978, pp. 721-725.
[84] S. W. Hawking, I. G. Moss and J. M. Stew
Review D, Vol. 26, 1982, pp. 2681-2713.
[85] S. W. Hawking, Physics Letters B, Vol. 231, 1989, pp.
237-239. doi:10.1016/0370-2693(89)90206-2
ies, Vol. 31,
atical Phy-
[86] Y. Zel’dovich and I. D. Navikov, “Stars and
University of Chicago Press, Chicago, 1971.
[87] T. Harada, Journal of Physics: Conference Ser
2006, pp. 111-114.
[88] S. W. Hawking, Communications in Mathem
sics, Vol. 43, 1975, pp. 199-220.
[89] D. N. Page, Physical Review D, Vol. 13, 1976, pp. 198-
206. doi:10.1103/PhysRevD.13.198
king, The Astrophysical Jour- [90] D. N. Page and S. W. Haw
nal, Vol. 206, 1976, pp. 1-7. doi:10.1086/154350
[91] D. B. Cline, The Astrophysical Journal, Vol. 501, 1998,
pp. L1-L3. doi:10.1086/311433
[92] P. Tisserand, et al., Astrophysics, Vol. 469, 2007, pp.
387-404. doi:10.1051/0004-6361:20066017
[93] M. Ricotti, J. P. Striker and J. K. Mack, The Astrophysi-
cal Journal, Vol. 680, 2008, pp. 829-845.
[94] R. W. Klebesadel, et al., The Astrophysical Journal, Vol.
182, 1973, pp. L85-L88. doi:10.1086/181225
., The Astrophysical Journal, Vol. [95] C. Kouveliotou, et al
413, 1993, pp. L101-L104. doi:10.1086/186969
[96] D. B. Cline, et al., International Journal of Astronomy
and Astrophysics, Vol. 1, 2011, pp. 164-172.
[97] N. Gehrels and P. Mészáros, Science, Vol. 337, 2012, pp.
932-936. doi:10.1126/science.1216793
[98] B. Zhang, Chinese Journal of Astronomy and Astrophy-
Copyright © 2013 SciRes. JMP
Copyright © 2013 SciRes. JMP
sics, Vol. 7, 2007, pp. 1-50.
[99] B. Zhang, Chinese Journal of Astronomy and Astrophy-
sics, Vol. 7, 2007, p. 329. doi:10.1088/1009-9271/7/2/18
ew of Astronomy and[100] N. Gehrels, et al., Annual Revi As-
trophysics, Vol. 47, 2009, pp. 567-617.
[101] G. Vedrenne and J.-L. Atteia, “Gamma-Ray Bursts,” Sprin-
ger, Berlin, 2009. doi:10.1007/978-3-540-39088-6
Cambridge [102] C. Kouveliotou, et al., “Gamma-Ray Bursts,”
University Press, Cambridge, 2012.
[103] S. E. Woosley, Astrophysical Journal, Vol. 405, 1993, pp.
[104] A. I. MacFadyen and S. E. Woosley, Astrophysical Jour-
nal, Vol. 524, 1999, pp. 262-289. doi:10.1086/307790
[105] R. D. Blandford and R. L. Znajek, Monthly Notices of the
Royal Astronomical Society, Vol. 179, 1977, pp. 433-456.
[106] W. H. Lee and E. Ramirez-Ruiz, New Journal of Physics,
Vol. 9, 2007, p. 17. doi:10.1088/1367-2630/9/1/017
[107] S. W. Hawking, Nature, Vol. 248, 1974, pp. 30-31.
[108] B. J. Carr, et al., Physical Review D, Vol. 81, 2010,
cle ID: 104019.
[109] J. B. Carr and S. W. Hawking, Monthly Notices of the
Royal Astronomical Society, Vol. 168, 1974, pp. 399
[110] D. B. Cline and W. P. Hong, Astrophysical Journal, Vol.
401, 1992, pp. L57-L60. doi:10.1086/186670