Journal of Modern Physics, 2012, 3, 1479-1486
http://dx.doi.org/10.4236/jmp.2012.310182 Published Online October 2012 (http://www.SciRP.org/journal/jmp)
String Cloud and Domain Walls with Quark
Matter in Lyra Geometry
Kamal Lochan Mahanta, Ashwini Kumar Biswal
Department of Mathematics, C. V. Raman College of Engineering, Bhubaneswar, India
Email: firstname.lastname@example.org, email@example.com
Received August 2, 2012; revised September 5, 2012; accepted September 15, 2012
We have constructed cosmological models for string cloud and domain walls coupled with quark matter in Lyra geome-
try. For this purpose we have solved the field equations using anisotropy feature of the universe, special law of variation
for Hubble’s parameter proposed by Berman  which yields constant deceleration parameter; and time varying dis-
. Further some properties of the obtained solutions are discussed.
Keywords: Cosmic Strings; Domain Walls; Quark Matter; Lyra Geometry
In order to geometrize the whole of gravitation and elec-
tromagnetism Weyl  proposed a modification of Rie-
mannian manifold. As this theory is physically unsatis-
factory, later on Lyra  proposed a further modification
of Riemannian geometry which bears a close resem-
blance to Weyl’s geometry. Sen  pointed out that the
static model with finite density in Lyra manifold is simi-
lar to the static model in Einstein theory. Halford 
showed that the vector field i in Lyra’s geometry
plays a similar role of cosmological constant Λ in general
theory of relativity. In addition he pointed out that the
energy conservation law does not hold in the cosmologi-
cal theory based on Lyra’s geometry. The scalar-tensor
theory of gravitation in Lyra manifold predicts the same
effects, within observational limits, as in Einstein theory
. Many authors [6-19] constructed different cosmo-
logical models and studied various aspects of Lyra’s
In field theories, topological defects are stable field
configurations with spontaneously broken discrete or
continuous symmetries [20,21]. Spontaneous symmetry
breaking is described within the particle physics context
in terms of the Higgs field. The symmetry is said to be
spontaneously broken if the ground state is not invariant
under the full symmetry of the Lagragian density. The
broken symmetries are restored at very high temperatures
in quantum field theories. The topology of the vacuum
1 is called domain walls [21,22],
called strings  and one dimensional
S called monopoles and two di-
mensional textures, and with 3
S is called three
dimensional textures. The topological defects are called
local or global depending on the symmetry is whether
local (gauged) or global (rigid). In the early universe
these defects are expected to be remnants of phase transi-
String theory attracted the attention of many authors as
it possesses the necessary degrees of freedom to describe
other interactions, even a mode to describe the graviton.
The presence of cosmic strings in the early universe is
considered using grand unified theories [25-30]. The
study of various aspects of cosmic strings in different
theories of relativity is available in the literature [31-52].
The topological defects such as strings, domain walls
and monopoles have an important role in the formation
of our universe, Hill et al.  pointed out that the for-
mation of galaxies are due to domain walls produced
during a phase transition after the time of recombination
of matter and radiation. Vilenkin  and Sikivie and
Ipser  discussed thin domain wall in Einstein’s the-
ory. Further Schmidt and Wang  discussed the same
in the context of Brans-Dicke theory. Widraw  ob-
tained that a thick domain wall with non-zero stress
along a direction perpendicular to the plane of the wall
does not allow static metric to be regular throughout en-
tire space. Goetz  constructed thick domain wall
cosmological model where the scalar field responsible
for the symmetry breaking is static while the metric de-
pends on time. Wang  obtained a class of exact solu-
tion to the Einstein’s field equations representing the
gravitational collapse of a thick domain wall. Rahaman et
al.  found an exact solution of the filed equations for
a thick domain wall in a five dimensional Kaluza-Klein
opyright © 2012 SciRes. JMP
K. L. MAHANTA, A. K. BISWAL
space time within the frame work of Lyra geometry.
Pradhan et al.  studiedplane symmetric domain wall
in Lyra geometry. Rahaman and Mukherji  con-
structed two models of domain walls in Lyra geometry. In
one of their model the space time is non-singular both in
its spatial and temporal behaviour and the gravitational
field experienced by a test particle is attractive. In the
other model they presented a spherical domain wall with
non vanishing stress components in the direction perpen-
dicular to the plane of the wall. Rahaman et al.  stu-
died two types of thin domain wall models in Lyra ge-
ometry. In their first model the pressure of the domain
wall is negligible along perpendicular and transverse
direction to the wall. In their second model pressure of the
domain wall in the perpendicular direction is negligible
but transverse pressures are existed. Further they showed
that the thin domain walls have no particle horizon and the
gravitational force due to them is attractive. Pradhan et al.
 obtained general solutions of the field equations for
bulk viscous domain walls in Lyra geometry.
It is believed that one of the transitions during the phase
transitions of the universe could be Quark Gluon Plasma
(QGP) hadron gas called quark-hadron phase transition
when cosmic temperature was T ~200 MeV. The quark-
hadron phase transition in the early universe and conver-
sion of neutron stars into strange ones at ultrahigh densi-
ties are two ways of formation of strange quark matter
[65-67]. In quark bag models based on strong interaction
theories it is considered that breaking of physical vacuum
takes place inside hadrons. As a result vacuum energy
densities inside and outside a hadron become essentially
different and the vacuum pressure on the bag wall equi-
librates the pressure of quarks and stabilizes the system. It
is pointed out that if the hypothesis of the quark matter is
true, then some of neutron stars could actually be strange
stars built entirely of strange matter [68,69]. The quark
matter is modeled with an equation of state (EOS) based
on phenomenological bag model of quark matter in which
quark confinement is described by an energy term pro-
portional to the volume. In the frame work of this model
the quark matter is composed of mass less u, d quarks,
massive s quarks and electrons. In the simplified version
of the bag model, assuming the quarks are mass
less and non-interacting we have 3
, where q
the quark energy density. The total energy density is given
and the total pressure by
Now from equations (1) and (2) we have
Again with the help of (41) and (43) we obtain
In this case domain walls behave like invisible matter
due to their negative tension. Further we find 3
proposed by Bodmer  and Witten .
3.2. Case 2
If we use (30) in (41) and (42) we get
222 222 22 22
nc ncnc nctt
In this case, when
with ne tension and dust quark matter. When
we get domain walls solutions
n anwe have domain walls solutions with negative tensiod
quark matter solution like radiation. When 2
tained exact solutions of the field eq-
loud and domain walls with quark
have stiff quark matter solution and domain walls disap-
In this paper we ob
uations for string c
matter in Lyra geometry. In our solutions we observe the
1) In the case of string cloud with quark matter for
, we get dust quark matter solution i.e. 0
this model the universe starts at an initial epoch tb
At initial epoch the physical parameters
verge. As cosmic time t gradually increases
decrease and finally they vanish when t. Tis is
consistent with the results of Brook-Have nationl
laboratory [80,81]. Here we find
. The present
upper limit of
is 10−15 obtained frndirect argu-
ments concernihe anisotropy of the primordial black
body radiation . The greater value of
model than the aforesaid limit indicates that e model
represents the early stages of the evolution of thuniverse.
At initial epoch tb
, the gauge function
With the increase in cosmic time t, gauge fnction u
decreases and drs as t . Hencehis theory
ed stiff domain wall solution. Since in the more
leads to Einstein general theory of relativity at infini
2) In the case of domain walls with quark matter we
alistic case in which the domain walls interact with the
primordial plasma, the equation of state for domain walls
is expected to be stiffer than that of a radiation, our solu-
tions correspond to the early stages of evaluation of the
universe. Here we note that the universe starts at an initial
. At the initial epoch the physical parame-
diverge. With the increase in cosmic
time t scalar expansion
and shear scalar 2
and fally thvanish as t.
In case 1 of strange quark matter coupleto domain
walls we get
as edpropos by Bodmer  and
Witten . Inse domain walls behave like invisi-
ble matter due negative tension.
In case 2 of aforesaid model when 2,
we get do-
main walls with negative tension and dust quark matter.
Copyright © 2012 SciRes. JMP
K. L. MAHANTA, A. K. BISWAL
, we have domain walls with negative ten-
sion anrk matter like radiation. When 2,
main walsappear and we have stiff quark matter. ls di
 H. Weyl, Sitzuss. Berlin, 1918, p.
etrie,” Mathematische Zeitschrift, Vol. 54, No. 1,
Here we observe that most of the propertf our
models are similar to the Kaluza-Klein cosmolog
odels (in string cloud and domain walls coupled with
quark matter) obtained earlier by Yilmaz  and Adhav
et al. .
ngsber Preuss Akad Wi
 G. Lyra, “Übereine Modifikation der Riemannschen
1951, pp. 52-64. doi:10.1007/BF01175135
 D. K. Sen, “A Static Cosmological Model,” Zeitschriftfür
Physik A Hadrons and Nuclei, Vol. 149, No. 3, 1957, pp
Australian Journal of Physics, Vol. 23, No. 5
urnal of Mathematical Physics
Review,” Fortschritte der Physik, Vol. 41, No
 W. D. Halford, “Cosmological Theory Based on Lyra’s
1970, pp. 863-870.
 W. D. Halford, “Scalar-Tensor Theory of Gravitation in a
Lyra Manifold,” Jo , Vol.
13, No. 11, 1972, pp. 1699-1704.
 A. Beesham, “FLRW Cosmological Models in Lyra’s
Manifold with Time Dependent ield,”
Australian Journal of Physics, Vol. 41, No. 6, 1988, pp.
 T. Singh and G. P. Singh, “Lyra’s Geometry and Cos-
8, 1993, pp. 737-764. doi:10.1002/prop.2190410804
 G. P. Singh and K. Desikan, “A New Class of Cosmo-
Logical Models in Lyra Geometry,” Pramana Journal of
Physics, Vol. 49, No. 2, 1997, pp. 205-212.
 A. Pradhan, L. Yadav and A. K. Yadav, “
mogeneous Universe with
a Bulk Viscous Fluid in Lyra
Geometry,” Astrophysics and Space Science, Vol. 299,
No 1, 2005, pp. 31-42. doi:10.1007/s10509-005-2795-x
 F. Rahaman, “Higher-Dimensional Global Monopole in
Lyra’s Geometry,” Fizika B, Vol. 11, No. 4, 2002, pp.
 F. Rahaman, S. Das, N. Begum and M. Hossain, “Higher
Dimensional Homogeneouscosmology in Lyra Geome-
try,” Pramana Journal of Physics, Vol. 61, No. 1, 2003,
pp. 153-159. doi:10.1007/BF02704519
 G. P. Singh, R. V. Deshpande and T. Singh, “Higher-
Dimensional Cosmological Model with Variable Gravita-
tional Constant and Bulk Viscosity in Lyra Geometry,”
Pramana Journal of Physics, Vol. 63, No. 5, 2004, pp.
 G. Mohanty, K. L. Mahanta and R. R. Sahoo, “Non-Ex-
istence of Five Dimensional Perfect Fluid Cosmological
Model in Lyra Manifold,” Astrophysics and Space Sci-
ence, Vol. 306, No. 4, 2006, pp. 269-272.
 G. Mohanty, K. L. Mahanta and B. K. Bishi, “Five Di-
mensional Cosmological Models in Lyra Geom
Time Dependent Displacement F
ield,” Astrophysics and
Space Science, Vol. 310, No. 3-4, 2007, pp. 273-276.
 G. Mohanty and K. L. Mahanta, “Five-Dimensional Axi-
ally Symmetric String Cosmological Model in L
Manifold,” Astrophysics and Spacyra
e Science, Vol. 312, No.
3-4, 2007, pp. 301-304. doi:10.1007/s10509-007-9691-5
 D. K. Sen and K. A. Dunn, “A Scalar-Tensor Theory of
Gravitation in a Modified Riemannian Manifold,” Jour-
nal of Mathematical Physics, Vol. 12, 1971, pp. 578-586.
 T. Singh and G. P. Singh, “Bianchi Type-I Cosmological
Models in Lyra’s Geometry,” Journal of Mathematical
Physics, Vol. 32, No. 9, 1991, pp. 2456-2458.
 T. Singh and G. P. Singh, “Bianchi Type-III and Kan-
towski-Sachs Cosmological Models in Lyra’s G
International Journal oeometry,”
f Theoretical Physics, Vol. 31, No.
8, 1992, pp. 1433-1446. doi:10.1007/BF00673976
 J. K. Singh and Sri Ram, “Spatially Homogeneous Cos-
mological Models in Lyra’s Geometry,” Il Nuovo Ci-
mento B, Vol. 112, No. 8, 1997, pp.1157-1162.
 A. Vilenkin and E. P. S. Shellard, “Cosmic Strings and
other Topological Defects,” Cambridge University Press,
 A. Vilenkin, “Cosmic Strings and Domain Walls,” Phys-
ics Reports, Vol. 121, No. 5, 1985, pp. 263-315.
rs, Vol. 48, No. 26,
 A. Vilenkin and A. E. Everett, “Cosmic Strings and Do-
main Walls in Models with Goldstone and Pseud
stone Bosons,” Physical Review Lette
1982, pp. 1867-1870. doi:10.1103/PhysRevLett.48.1867
 R. Rajaraman, “Solutions and Instantons,” North-Holland,
 T. H. R. Skyrme, “Particle States of a Quantized Meson
Field,” Proceedings of the Royal Society A, Vol. 262, No.
1309, 1961, pp. 237-245.
 T. W. B. Kibble, “Topology of Cosmic Domains and
Strings,” Journal of Physics A, Vol. 9, No. 8, 1976, p.
 A. Vilkenkin, “Cosmic Strings,” Physical Review D, Vol.
24, No. 8, 1982, pp. 2082-2089.
 A. E. Everett, “Cosmic Strings in Unified Gauge Theo-
ries,” Physical Review D, Vol. 24, No. 4, 1981, pp. 858-
dinburgh, 1981, p. 201.
 Ya. B. Zeldovich, I. Yu. Kobzarev and L. B. Okun, Zh.
Eksp. Teor. Fiz., Vol. 67, 1974, p. 3
 Ya. B. Zeldovich, I. Yu. Kobzarev and L. B. Okun, Sov.
Phys. JETP, Vol. 40, 1975, p. 1.
 J. Ellis, “Gauge Theories and Experiments at High Ener-
gies,” Proceedings of the 21st Scottish University Sum-
mer School, SUSSP Publication, E
 J. Stachel, “Thichening the String. I. The String Perfect
Dust,” Physical Review D, Vol. 21, No. 8, 1980, pp.
Copyright © 2012 SciRes. JMP
K. L. MAHANTA, A. K. BISWAL 1485
 P. S. Letelier, “String Cosmologies,” Physical Review D,
Vol. 28, No. 10, 1983, pp. 2414-2419.
 C. J. Hogan and M. J. Rees, “Gravitational Interactions of
Cosmic Strings,” Nature, Vol. 311, 1984, pp. 109-114.
 Y. S. Myung, B. H. Cho, Y. Kim and Y. J. Park, “Entropy
Production of Superstrings in Thevery Early Universe
Physical Review D, Vol
. 33, No. 10, 1986, pp. 2944-2947.
 K. D. Krori, T. Chaudhury, C. R. Mahanta and A. Ma-
zumdar, “Some Exact Solutions Instring Cosmology,”
General Relativity and Gravitation, Vol. 22, No. 2, 1990,
pp. 123-130. doi:10.1007/BF00756203
 C. Gundalach and M. E. Ortiz, “Jordan-Brans-Dicke
Cosmic Strings,” Physical Review D, Vol. 42, No. 8,
1990, pp. 2521-2526. doi:10.1103/PhysRevD.42.2521
 A. Barros and C. Romero, “Cosmic Vacuum Strings and
Domain Walls in Brans-Dicke Theory of Gravity,” Jour-
nal of Mathematical Physical, Vol. 36, No. 10, 1995, pp
 I. Yavuz anf I. Yilmaz, “Some Exact Solutions of String
Cosmology with Heat Flux in Bianchi Type III Space
time,” Astrophysics and Space Science, Vol. 245, No. 1,
1996, pp. 131-138. doi:10.1007/BF00637808
 A. Banerjee, N. Banerjee and A. A. Sen, “Static and Non-
static Global String,” Physical Review D, Vol. 53, No. 10,
1996, pp. 5508-5512. doi:10.1103/PhysRevD.53.5508
 D. R. K. Reddy, “Plane Symmetric Cosmic Strings in
Lyra Manifold,” Astrophysics and Space Science, Vol.
300, No. 4, 2005, pp. 381-386.
 J. M. Nevin, “String Dust Solutions of the Einstein’s
Field Equations with Spherica
Symmetry,” General Relativity a
l and Static Cylindrical
nd Gravitation, Vol
No. 3, 1991, pp. 253-260. doi:10.1007/BF00762288
 S. Chakraborty, “A Study on Bianchi-IX Cosmological
Model,” Astrophysics and Space Science, Vol. 180, No. 2,
1991, pp. 293-303. doi:10.1007/BF00648184
 R. Tikekar and L. K. Patel, “Some Exact Solutions of
String Cosmology in Bianchi III Spacetime,” General
Relativity and Gravitation, Vol. 24, No. 4, 1992, pp. 397-
 G. Mohanty, R. R. Sahoo and K. L. Mahanta, “Five Di-
mensional LRS Bianchi Type-I String Cosmological
Model in Saez and Ballester Theory,” Astrophysics and
Space Science, Vol. 312, No. 3-4, 2007, pp. 321-324.
 G. Mohanty and R. R. Sahoo, “Incompatibility of Five
Dimensional Lrs Bianchi Type-V String and Meso
String Cosmological Models in
trophysics and Space Science, Vol. 315, No. 1-4, 2008,
pp. 319-322. doi:10.1007/s10509-008-9835-2
 R. Bali and R. D. Upadhaya, “An LRS Bianchi Type I
Bulk Viscous Fluid String Cosmological Model in Gen-
eral Realtivity,” Astrophysics and Space Science
288, No. 3, 2003, pp. 287-292.
 X. X. Wang, “Exact Solutions for String Cosmology,”
Chinese Physical Letters, Vol. 20, No. 5, 2003, pp. 615-
 X. X. Wang, “Kantowski-Sachs String Cosmological
Model with Bulk Viscosity in General Relativity,” As-
trophysics and Space Science, Vol. 298, No. 3, 2005, pp.
 A. Pradhan and P. Mathur, “Magnetized String Cosmo-
logical Model in Cylindrically Symmetric Inhomogene-
ous Universe-Revisited,” Astrophysics and Space Science,
Vol. 318, No. 3-4, 2008, pp. 255-261.
 A. Pradhan, “Some Magnetized Bulk Viscous String
Cosmological Models in Cylindrically Symmetric Inho-
mogeneous Universe with Variable Λ Term
cations in Theoretical Physics, V
ol. 51, No. 2, 2009, pp.
 H. Amirashchi and H. Zainuddin, “Magnetized Bianchi
Type III Massive String Cosmological Models in General
Relativity,” International Journal of Theoretical Physics,
Vol. 49, No. 11, 2010, pp. 2815-2828.
 S. K. Tripathy. S. K. Sahu and T. R. Routray, “String
Cloud Cosmologies for Bianchi Type-III Models with
Electromagnetic Field,” Astrophysics a
Vol. 315, No. 1-4, 2008, pp. 105-110.
nd Space Science,
 C. T. Hill, D. N. Schramm and J. N. Fry, “Cosmological
Structure Formation from Soft Topological Defects,”
Comments on Nuclear and Particle
1989, p. 25. Physics, Vol. 19,
 A. Villenkin, “Gravitational Field of Vacuum Domain
Walls,” Physics Letters B, Vol. 133, No. 3-4, 1983, pp.
 J. Ipser and P. Sikivie, “Gravitationally Repulsive Do-
main Wall,” Physical Review D, Vol. 30, No. 4, 1984, pp.
 H. Schmidt and A. Wang, “Plane Domain Walls When
Coupled with the Brans-Dicke Scalar Fields,” Physical
Review D, Vol. 47, No. 10, 1984, pp. 4425-4432.
 L. M. Widrow, “General-Relativistic Domain Walls,”
Physical Review D, Vol. 39, No. 12, 1989, pp. 3571-3575.
 G. Goetz, “The Gravitational Field of Plane Symmetric
Thick Domain Walls,” Journal of Mathematical Physics,
Vol. 31, No. 11, 1990, pp. 2683-2687.
 A. Wang, “Gravitational Collapse of Thick Domain Walls:
An Analytic Model,” Modern Physics Letters A, Vol. 9,
No. 39, 1994, pp. 3605-3609.
, No. 3-4, 2003,
 F. Rahaman, P. Ghosh, S. Shekhar and S. Mal, “Higher
Dimensional Thick Domain Wall in Lyra Geometry,” As-
trophysics and Space Science, Vol. 286
pp. 373-379. doi:10.1023/A:102635
 A. Pradhan, I. Aotemshi and G. P. Singh, “Plane Sym-
metric Domain Wall in Lyrageometry,” Astrophysics and
Copyright © 2012 SciRes. JMP
K. L. MAHANTA, A. K. BISWAL
Copyright © 2012 SciRes. JMP
Space Science, Vol. 288, No. 3, 2003, pp. 315-325.
 F. Rahaman and R. Mukherji, “Domain Walls in Lyra
Geometry,” Astrophysics and Space Science, Vol. 288,
No. 4, 2003, pp. 389-397.
 F. Rahaman, M. Kalam and R. Mandal, “Thin Domain
Walls in Lyra Geometry,” Astrophysics and Space Sci-
ence, Vol. 305, No. 4, 2006, pp. 337-340.
 A. Pradhan, K. K. Rai and A. K. Yadav, “Plane Symmet-
ric Bulk Viscous Domain Wall in Lyra Geometry,” Bra-
zilian Journal of Physics, Vol. 37, No.
3b, 2007, pp.
 N. Itoh, “Hydrostatic Equilibrium of Hypothetical Quark
Stars,” Progress of Theoretical Physics, Vol. 44, No. 1,
1970, pp. 291-292. doi:10.1143/PTP.44.291
 A. R. Bodmer, “Collapsed Nuclei,” Physical Review D,
Vol. 4, No. 6, 1971, pp. 1601-1606.
 E. Witten, “Cosmic Separation of Phases,” Physical Re-
view D, Vol. 30, No. 2, 1984, pp. 272-285.
 C. Alcock, E. Farhi and A. Olinto, “Strange Stars
s, Vol. 160, No. 1, 1986
ls by Gravitational Wave Observation,”
Astrophysical Journal, Vol. 310, 1986, pp. 261-272.
 P. Haensel, J. L. Zdunik and R. Schaefer, “S
stars,” Astronomy & Astrophysic
 J. Kapusta, “Finite Temperature Field Theory,” Ca
bridge University Press, Cambridge, 1994.
 H. Sotani, K. Kohri and T. Harada, “Restricting Quark
Physical Review D, Vol. 69, No. 8, 2004, Article ID:
 I. Yilmaz, “Domain Walls Solutions in the Non-Static
and Stationary Godel Universes with a Cosmological
Constant,” Physical Review D, Vol. 71, No. 10, 2005, Ar-
ticle ID: 103503. doi:10.1103/PhysRevD.71.103503
 I. Yilmaz, “String Cloud and Domain Walls with Quark
Matter in 5-D Kaluza-Klein Cosmological Model,” Gen-
eral Relativity and Gravitation, Vol. 38, No. 9, 2006, pp.
 K. S. Adhav, A. S. Nimkar and M. V. Dawande, “String
Cloud and Domain walls with Quark Matter in n-Dimen-
sional Kaluza-Klein Cosmological Model,” International
Journal of Theoretical Physics, Vol. 47, No. 7, 2008, pp.
 G. S. Khadekar, R. Wanjari and C. Ozel, “Domain Wall
with Strange Quark Matter in Kaluza-Klein Type Cos-
mological Model,” International Journal of Theoretical
Physics, Vol. 48, No. 9, 2009, pp. 2550-2557.
 K. L. Mahanta, S. K. Biswal, P. K. Sahoo and
hikary, “String Cloud with Quark
M. C. Ad-
Matter in Self- Creation
Cosmology,” International Journal of Theoretical Phys-
ics, Vol. 51, No. 5, 2012, pp. 1538-1544.
 R. Bali, “Magnetized Cosmological M
tional Journal of Theoretical Podel,” Interna-
hysics, Vol. 25, No. 7,
1986, pp. 755-761. doi:10.1007/BF00668721
 M. S. Berman, “A Special Law of Variation for Hubble’s
Parameter,” Il Nuovo Cimento B, Vol. 74, No. 2, 1983, pp.
rld and Nonsingular Cosmological Models,”
 N. Okuyama and K. Maeda, “Domain Wall Dynamics in
Physical Review D, Vol. 70, No. 6, 2004, Article ID:
 B. B. Back, et al., “The PHOBOS Perspective on Dis-
coveries at RHIC,” Nuclear Physics A, Vol. 757, No. 1-2,
ch for the Quark-Gluon Plasma: The
gies,” General Relativ-
2005, pp. 28-101.
 J. Adam, et al., “Experimental and Theoretical Chal-
lenges in the Sear
STAR Collaboration’s Critical Assessment of the Evi-
dence from RHIC Collisions,” Nuclear Physics A, Vol.
757, No. 1-2, 2005, pp. 102-183.
 C. B. Collins, E. N. Glass and D. A. Wilkinson, “Exact
Spatially Homogeneous Cosmolo
ity and Gravitation, Vol. 12, No. 10, 1980, pp. 805-823.