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A new alternative cosmological model called black hole universe was recently developed by the author on the basis of the following three fundamentals: 1) the principle of spacetime black hole equivalence, 2) the cosmological principle of spacetime isotropy and homogeneity, and 3) the Einsteinian general theory of relativity that describes the effect of matter on spacetime. According to this black hole model of the universe, the author up-to-dately has self-consistently described the origin, structure, evolution, expansion, and acceleration of the universe, quantitatively explained the measurements of cosmic microwave background radiation, type Ia supernovae’s luminosity distance and redshift, and dynamic properties of star-like, massive, and supermassive black holes such as gamma-ray bursts, X-rays flares from galactic centers, and quasars, and fully overcome the difficulties of the conventional model of the universe such as the problems of horizon, flatness, monopole, inflation, dark matter, dark energy, and so on. In this paper, the author will examine and overview thoroughly this new cosmological model and completely describe its development from the three fundamentals and its creative explanations to the existing observations of the universe. From this comprehensive investigation of the new cosmological model, the author will further reveal the fundamental regularities and laws of the black hole universe with respect to the spacetime mass and radius, spacetime equilibrium, spacetime expansion and acceleration, spacetime radiation energy, and spacetime entropy variation. These efforts will help us to uncover various regularities and mysteries of the universe.

Brewing the idea―the universe as a black hole―that was unexpectedly emerged from his mind in 2004 at reading the famous paper entitled “Mach’s principle and a relativistic theory of gravitation [^{th} American Astronomical Society (AAS) meeting held at Austin, Texas (USA), on January 7-11, 2008 [^{th} AAS meeting held at Boston, Massachusetts (USA), on June 1-5, 2014. In this special session of the 224^{th} AAS meeting, many famous cosmologists from the world were brought together to discuss cosmological issues of multiverse [

The early studies done by the author up to the date have 1) self-consistently described the origin of the universe from black holes, the structure of the entire space with infinite layers, the iterative and cyclic evolution in an endless and beginningless style, and the physical expansion outward in one-way along the time or entropy increasing direction, 2) quantitatively explained the measurement of 2.725 K cosmic microwave background radiation with the blackbody spectrum, the observation of type Ia supernovae’s luminosity distance and redshift for the acceleration of the universe, and the dynamic properties of star-like, massive, and supermassive black holes such as gamma-ray bursts, X-rays flares from galactic centers, and quasars, and 3) fully overcome the difficulties of the conventional standard big bang model of the universe such as the problems of the horizon, flatness, monopole, inflation, dark matter, dark energy, and so on. The results obtained from these early studies have been presented in a sequence of AAS meetings [

The big bang model of the universe, though being the currently accepted standard cosmological model, critically relies on a growing number of hypothetical entities [

problems such as the horizon, flatness, and monopole problems [

In the black hole model of the universe [

The first principle or fundamental of black hole universe is the principle of spacetime black hole equivalence. More specifically, a black hole constructs an individual spacetime and a spacetime encloses a black hole. Black holes and spacetimes are equivalent (

result of Einstein’s general theory of relativity and Schwarzschild’s solution of the field that a region, where matter accumulates up to a critical point such that the mass-radius ratio is equal to M/R = c^{2}/2G ~ 6.75 ~ 10^{26} kg/m (or ~0.3375 solar masses/km), forms a black hole and meantime builds or constructs its own space being singular to the outside and its own time being noncausal to the outside. When a black hole is formed, an individual spacetime is immediately wrapped. Here c is the speed of light traveling in the free space and G is the gravitational constant.

According to this newly proposed principle, our four-dimensional (4D) spacetime universe is a black hole, extremely supermassive and fully expanded. All the inside, currently observed, star-like, massive, and/or supermassive black holes are subspacetimes of our black hole universe (

The spatial boundary of a spacetime or black hole including our black hole universe is the Schwarzschild absolute event horizon determined by [

2 G M c 2 R = 1 (1)

where M and R are the mass and radius of the spacetime or black hole. This mass-radius relation is also the relation of the effective mass and radius of the universe from the Mach principle [^{th} law of the black hole universe.

Therefore, the black hole model of the universe does not exist the horizon problem. Within a black hole or a spacetime, an event occurred at one point is observable to all other points and events occurred at different points are all causally related one another.

Equation (1) indicates that the radius of a spacetime or black hole including the black hole universe is proportional to its mass (R µ M), i.e. the ratio remains a constant or is conserved. For a star-like black hole with 3 solar masses, its radius is about 9 km. For a supermassive black hole with 3 billion solar masses, its radius is about 9 × 10^{9} km. For the present black hole universe with hundred billion trillion solar masses, its radius is about 10^{23} km. The black hole model of the universe is supported by the Mach principle, the observations of the universe, and the Einsteinian general theory of relativity.

A black hole curves the spacetime maximally, so that it becomes singular and noncausal to the outside. It is highly curved, wrapped and closed. The 3D space curvature constant of a closed spacetime or a black hole including our black hole universe is

k = 1 (2)

Therefore, the black hole model of the universe does not exist the flatness problem. Having neither the horizon problem nor the flatness problem, the black hole model of the universe does not need an inflation epoch, a nonphysical process that the current widely accepted big bang model of the universe is relying on [

It is reasonable to suggest that our black hole universe was originated from a star-like black hole with several solar masses, which was formed from a massive star when the inside thermonuclear fusion has completed, and grew up through a supermassive black hole with billions of solar masses to the present state with hundred-billion-trillions of solar masses, by accreting the ambient matter or merging with other black holes (

The second principle or fundamental of black hole universe is the cosmological principle of spacetime isotropy and homogeneity. This is also one of the two fundamentals in the big bang theory. According to this principle, a spacetime or black hole including our black hole universe, if it is viewed on a scale that is sufficient large or comparable to the scale of the spacetime, is homogeneous and isotropic. This principle implies that there is no special location and direction in a spacetime or black hole including the black hole universe. The properties of the universe are the same for all observers in the universe. More strongly, physical laws are all universal. If a physical law is applicable to the earth, then it can be applied to everywhere.

The metric of an isotropic and homogeneous spacetime or black hole including our black hole universe is given by the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric [

d s 2 = c 2 d t 2 − R 2 ( t ) [ d r 2 1 − k r 2 + r 2 ( d θ 2 + s i n 2 θ d ϕ 2 ) ] (3)

where ds is the line element of 4D spacetime, r, θ, ϕ are co-moving space-coordinates, t is the time, R(t) is the radius of curvature of the space, and k is the curvature constant of the space. In the black hole model of the universe, R(t) is the radius of the black hole or spacetime and k = 1.

The density of matter (ρ, defined as mass M divided by the volume V) in an isotropic and homogeneous spacetime or black hole including our black hole universe can be determined as

ρ ≡ M V = 3 c 6 32 π G 3 M 2 = 3 c 2 8 π G R 2 (4)

i.e. ρ R 2 = constant and ρ M 2 = constant . Here, we have applied the Mach-Schwarzschild M-R relation (Equation (1)) and V = 4 π R 3 / 3 . It is seen that the density of matter in a spacetime is inversely proportional to the square of the mass ( ρ ∝ M − 2 ) or the square of the radius ( ρ ∝ R − 2 ). Both the mass and radius of the universe can be determined from the density of the universe. According to the current observations of the universe, the density of the present universe ρ 0 is about the critical density ρ 0 ~ ρ C ≡ 3 H 0 2 / ( 8 π G ) ~ 9.2 × 10 − 27 kg / m 3 . Then, from Equation (4), we can determine the radius and mass of the present universe as R 0 = 3 c 2 / ( 8 π G ρ 0 ) ~ 1.32 × 10 26 m (or ~14 billion light years) and M 0 = R 0 c 2 / ( 2 G ) ~ 8.8 × 10 52 kg , respectively.

the mass of the universe and thus cannot determine the radius of the present universe according to the measurement of the density. Equation (4) can be considered as another form of the 0^{th} law of black hole universe.

The theory or third fundamental of black hole universe is the Einsteinian general theory of relativity, which is a theory of spacetime or a geometric theory of gravitation that describes the effect of matter on spacetime [

G μ ν = 8 π G c 4 T μ ν (5)

where G_{μν} is the Einsteinian curvature tensor of spacetime and T_{μν} is the energy-momentum tensor of matter in spacetime. Einstein’s another theory called special relativity describes the effect of motion on spacetime [

The theoretical predictions of general relativity such as the gravitational redshift of light from the Sun, the deflection of starlight by the Sun, the precessions of planetary perihelia, and the time delays of radar echoes have been confirmed in all observations and experiments to date. The Schwarzschild metric solution of the Einsteinian field equation of general relativity implies the existence of black holes, regions of space in which space and time are distorted in such a way that nothing, not even light, can escape from [

Substituting the FLRW metric of spacetime (Equation (3)) into the Einsteinian field equation of general relativity (Equation (5)), we have the Friedmann equation [

H 2 ( t ) ≡ R ˙ 2 ( t ) R 2 ( t ) = 8 π G ρ ( t ) 3 − c 2 R 2 ( t ) (6)

where H ( t ) is the Hubble parameter or the expansion rate of the universe. The dot sign refers to the derivative with respect to time, R ˙ ( t ) ≡ d R ( t ) / d t . The Hubble constant H 0 is the expansion rate of the universe at the present time and was measured as H 0 ~ 70 km/s/Mpc [

Substituting the density equation (Equation (4)) into the Friedmann equation (Equation (6)), we have

R ˙ ( t ) = 0 or H ( t ) = 0 (7)

This implies that an individual spacetime or black hole including our black hole universe, if there is not any external influence, is in the static state and equilibrium. A black hole in the static or equilibrium state is quite or does not emit. We here call this regularity as the law of spacetime equilibrium (or the 1^{st} law of black hole universe). To have a static universe, Einstein [

This law of spacetime equilibrium has overturned the traditional idea that all the matter inside a black hole is piled up in a singular point at the center, while other parts are empty, though nobody understands how this central singularity works. According to this law, the matter inside a black hole is homogeneously and isotropically distributed in the spacetime that the black hole forms. The spacetime formed by a black hole is highly curved and power enough to hold or sustain exactly all the matter of the black hole that forms the spacetime. The gravity of the matter inside a black hole is balanced by the curvature of the spacetime formed by the black hole. This does not exclude any possible anisotropy and inhomogeneity in a small scale, a scale that is significantly smaller than the scale of the spacetime formed by the black hole. The balance force produced by a highly curved spacetime (here we name it as the spacetime tension) prevents the matter of black hole from further crunching to the center to form a singular point. This is analogy to that a spring or string, when stretched by an object that is hung on, produces a tension that prevents the object from falling to the ground.

When a spacetime or black hole including our black hole universe accretes matter from the outside or merges with other black holes, it becomes dynamic and expands [

2 G ( M ( t ) + d M ( t ) ) c 2 R ( t ) > 1 (8)

In this case, the spacetime breaks its equilibrium state and expands its size or radius from R ( t ) to R ( t ) + d R ( t ) , where the radius increment d R ( t ) can be determined by

2 G ( M ( t ) + d M ( t ) ) c 2 ( R ( t ) + d R ( t ) ) = 1 (9)

Substituting the Mach-Schwarzschild M-R relation Equation (1) into Equation (9), we have

2 G c 2 d M ( t ) d R ( t ) = 1 (10)

Therefore, a spacetime or black hole including our black hole universe expands when it inhales matter from the outside. The expansion rate (or the rate of change in radius) is obtained as

R ˙ ( t ) = 2 G c 2 M ˙ ( t ) (11)

and the Hubble parameter is given by

H ( t ) ≡ R ˙ ( t ) R ( t ) = M ˙ ( t ) M ( t ) (12)

Equation (11) or Equation (12) indicates that the rate, at which a spacetime or black hole including the black hole universe expands, is proportional to the rate, at which it inhales matter from the outside. We here define this relation as the law of spacetime expansion, M ˙ ( t ) = H ( t ) M ( t ) or R ˙ ( t ) = H ( t ) R ( t ) . A spacetime or black hole becomes dynamic when it accretes matter. A dynamic spacetime expands due to non-equilibrium.

Considering that a black hole with three solar masses accretes matter at a rate of 10^{−5} solar masses per year from its outside [^{5} solar masses in one second, or swallows a supermassive black hole in about a few hours. If Λ is introduced to the Einsteinian field equation, the black hole universe model determines it as Λ = 3 H 0 2 = 3 ( M ˙ 0 / M 0 ) 2 ~ 1.5 × 10 − 35 s − 2 .

To expand, a spacetime or black hole including our black hole universe must have an outside, where matter is available for accretion and other black holes or parallel universes for mergers. Therefore, the black hole model of the universe suggests that the entire space is structured with layers, hierarchically and family-likely built [

To see the multilayer structure of the space in a larger (or more complicate) view, we plot, in

The evolution of the space structure is iterative [

universes (i.e. the inside star-like and supermassive black holes) grow and merge each other into a new universe. Therefore, when one universe expands out, a new similar universe is born from inside. Like the living things in the nature, the universe passes through its own birth, growth, and death process and iterates this process endlessly. Its structure evolves iteratively forever without the beginning and end.

There is nothing more natural than to consider the entire space to be infinite large without an edge and have infinite number of layers [

The black hole universe model gives a fantastic structure of the whole space. All universes are self-similar and governed by the same physics, the Einsteinian general theory of relativity with the FLRW metric, Mach-Schwarzschild M-R relation, and positive curvature constant. The expansion of a black hole universe increases its mass and radius and decreases its density and temperature, but it does not alter the laws of physics. This infinite hierarchically layered space can also be represented as

n i is the number of universes in the i^{th} layer, and L refers to the number of layers in the whole space. For the four layer (or generation) black hole universes sketched in

When a spacetime or black hole including our black hole universe accretes matter in an increasing rate, i.e. M ¨ ( t ) > 0 , it accelerates its expansion [^{nd} law of black hole universe. The dimensionless deceleration parameter is usually defined as

q ( t ) ≡ − R ( t ) R ¨ ( t ) R ˙ 2 ( t ) = − M ( t ) M ¨ ( t ) M ˙ 2 ( t ) (13)

where the double dot sign refers to the second order derivative with respect to time. From Equation (13), we see that whether the black hole universe accelerates or not depends on whether the double dot of mass is positive or not. For a positive M ¨ ( t ) > 0 , we have a negative deceleration parameter q ( t ) < 0 , i.e. acceleration of the universe.

According to the type Ia supernova measurements and their empirical distance-redshift relation, Daly et al. [^{2} (or about 110 solar masses per year square).

To explain the type Ia supernova measurements in accordance with the black hole universe model, we first solve Equation (13) to find the mass and Hubble parameter as functions of time. For a constant acceleration expansion universe, the time-dependent mass can be analytically solved from Equation (13) as,

M ( t ) = M 0 [ ( q + 1 ) H 0 t + 1 ] 1 q + 1 (14)

from which the Hubble parameter is derived as

H ( t ) = M ˙ ( t ) M ( t ) = H 0 ( q + 1 ) H 0 t + 1 (15)

The time t can be replaced by the redshift z, because

1 + z ≡ R 0 R ( t ) = M 0 M ( t ) = [ ( q + 1 ) H 0 t + 1 ] − 1 q + 1 (16)

This mass-redshift relation, M ( t ) = M 0 / ( 1 + z ) , does not depend on the deceleration parameter q. Using Equation (16) to replace the time of Equation (15), we obtain

H ( z ) = H 0 ( 1 + z ) q + 1 (17)

To explain the type Ia supernova measurements according to the black hole universe model, we then determine the luminosity distance-redshift relation from the mass-time relation Equation (14) as

d L = ( 1 + z ) R 0 s i n [ ∫ t 0 c d t R ( t ) ] = ( 1 + z ) R 0 s i n [ ∫ t 0 c 3 d t 2 G M ( t ) ] (18)

Substituting Equation (14) into Equation (18), completing the integration and then using Equation (16), we have

d L = ( 1 + z ) R 0 s i n [ c 3 2 G M 0 H 0 1 − ( 1 + z ) − q q ] (19)

This redshift and luminosity distance relationship (Equation (19)) reduces to the Hubble law z = d L H 0 / c at z ≪ 1 .

Recently, the author pointed out that the luminosity distance-redshift relation that was usually applied to analyze the measurement of distant type Ia supernovae is an approximate expression that is only valid for nearby objects with

z ≪ 1 [

In the black hole universe model, if we include this redshift factor, the luminosity distance expression (Equation (19)) becomes,

d L = ( 1 + z ) 3 / 2 R 0 s i n [ c 3 2 G M 0 H 0 1 − ( 1 + z ) − q q ] (20)

Using this equation, we can also nicely fit the data of type Ia supernovae if the deceleration parameter is chosen about q = 0.5 (see

According to Planck’s law, the spectral energy density of the blackbody radiation within a black hole including the black hole universe can be written as

u ( ν , T ) = 8 π h ν 3 c 3 1 e x p ( h ν k B T ) − 1 (21)

where ν is the radiation frequency, T is the temperature, h is the Planck constant, and k B is the Boltzmann constant. In the SI unit system, the unit of u ( ν , T ) is J/m^{3}/Hz. ^{4}, 10^{8}, and 10^{12} K, respectively [

Integrating the spectral energy density (Equation (21)) with respect to the frequency of radiation in the entire range, we have the energy density of the blackbody radiation inside a black hole including the black hole universe,

ρ γ ≡ U V = 8 π 5 k B 4 15 h 3 c 3 T 4 = β T 4 (22)

where U is the total radiation energy inside the black hole, V is the volume of the black hole, and the constant β is given by β ≡ 8 π 5 k B 4 / ( 15 h 3 c 3 ) ~ 7.54 × 10 − 16 J/m^{3}/K^{4}. Inside a black hole with the four temperatures given in ^{−14}, 7.54, 7.54 × 10^{16}, 7.54 × 10^{32} J/m^{3}, respectively.

As a spacetime or black hole including the black hole universe accretes its outside matter and radiation, it expands its volume from V to V + dV or radius from R to R + dR. This type of expansion does not geometrically stretch the space of itself, instead it just takes the space as well as the matter and radiation from the outside. Considering that the increase of the Planck radiation energy within the black hole equals to the radiation energy inhaled from the outside space, we have

β ( T + d T ) 4 ( V + d V ) − β T 4 V = β T p 4 d V (23)

where T is the temperature of the black hole, dT is the change (or decrease because it is negative) of the temperature due to the expansion of the black hole, and T p is the temperature outside the black hole, i.e. the temperature of the mother black hole or universe. Since d V / V = 3 d R / R , we can reform Equation (23) by a first order development as

d T d R = − 3 T 4 R [ 1 − ( T p T ) 4 ] (24)

This equation governs the thermal history of the black hole universe that grew up from a star-like black hole through a supermassive black hole and a mini universe to the present state [

For hot star-like or supermassive black holes, the temperatures inside should be much greater than the temperatures outside, i.e. T ≫ T p . In this case Equation (24) approximately reduces to

d T d R = − 3 T 4 R (25)

which can be simply solved as

R 3 T 4 = C (26)

where C is an integral constant. Therefore, the temperature of a star-like or supermassive black hole decreases as it expands in size according to T ∝ R − 3 / 4 . Substituting Equation (26) into Equation (22), we obtain the total radiation energy inside a star-like or supermassive black hole to be a constant and thus independent of its size,

U = V β T 4 = 4 3 π β R 3 T 4 = 4 3 π β C = Constant (27)

This interesting result indicates that the blackbody radiation energy inside a star-like or supermassive black hole remains the same no matter it is static or dynamic. Attaining matter and growing its size do not increase its total radiation energy. Here, we call this regularity of constant radiation energy as the law of radiation energy conservation (or the 3^{rd} law of black hole universe).

^{12} K, the blackbody radiation dominates at the frequency of gamma rays. The radiation maximizes its spectral energy density up to ~10^{25} J/m^{3}/Hz at frequency of ~10^{23} Hz. Inside a massive or supermassive black hole with temperature of 10^{8} K, the blackbody radiation dominates at the frequency of X-rays. The radiation maximizes its spectral energy density up to ~10^{12} J/m^{3}/Hz at frequency of ~10^{19} Hz.

A black hole, when it accretes its ambient matter or merges with another black hole, becomes dynamic. A dynamic black hole has a broken event horizon and thus cannot hold the inside hot (or high-frequency) blackbody radiation, which flows or leaks out of it and produces X-ray flares or gamma ray bursts. Dynamic star-like black holes with thousand billions of Kelvins (i.e. ~10^{12} K) radiate gamma rays, while dynamic massive or supermassive black holes with hundred millions of Kelvins (i.e. ~10^{8} K) radiate X-rays such as X-ray emissions from

quasars, supermasive black holes with billions of solar masses, and X-ray flares from Sagitarius A*, a massive black hole with millions of solar masses at the Milky Way center. This section describes how these dynamic properties of black holes are explained according to the black hole model of the universe [

To reveal the possible thermal history of the black hole universe, we have considered a general case that the black hole universe decreases its relative temperature in a rate slightly greater than the mother universe as [

d T p T p = q d T T (28)

which is equivalent to

T p = α T q or T p T = α T − δ (29)

Here q is a constant slightly less than 1; δ ≡ 1 − q is a small number; and α can be derived from q or δ according to the temperature and radius of the present universe. The other cases such as q = 1 or q to be significantly smaller than the unity could not explain the measurement of cosmic microwave background radiation as shown in [

In this case with q slightly smaller than the unity, the solution of Equation (24) can be analytically obtained as

T = R − 3 / 4 ( α 4 R 3 δ + T s 4 δ R s 3 δ ) 1 / 4 δ (30)

where the constant α is given by

α = [ T 0 4 δ − ( R s R 0 ) 3 δ ] 1 / 4 (31)

Choosing q or δ appropriately, we can completely determine the thermal history of the black hole universe that evolved from a hot star-like black hole with temperature T s and radius R s to the present universe with temperature T 0 and radius R 0 . In

It is seen that all temperature lines are concave downward and approach ~2.725 K as the black hole universe expands to the present size. Therefore, the initial temperature of the star-like black hole T s is not critical to the present universe. The reason is because most matter and radiation are from the mother universe. This reason also explains why all other physical properties of the star-like black hole, including its size (or mass), angular momentum, and charge, and the evolution of the early universe are not critical to the present universe. Furthermore, the early process of material accretion and black hole mergers do not have significant leftover in the present universe.

A spacetime or black hole including our black hole universe expands when it accretes matter and radiation from its outside. The expansion also alters its entropy given by [

d S ≡ d Q T = c 2 T d M + β T b 4 T d V = ( c 4 2 G T + 4 π β T b 4 R 2 T ) d R (32)

The first term of Equation (32) is the entropy increase due to the accretion of matter and the second term of Equation (32) is the entropy increase due to the accretion of radiation. It is seen from Equation (32) that the entropy of a spactime or black hole including our black hole universe does not decrease, d S ≥ 0 , because d R ≥ 0 . This regularity is called the law of spactime entropy increase (or the 4^{th} law of black hole universe).

Integrating Equation (32), we have the entropy of a spacetime or black hole with radius R or mass M = c 2 R / ( 2 G ) ,

S − S s = ∫ R s R ( c 4 2 G T + 4 π β T b 4 R 2 T ) d R (33)

where S s is the entropy of the reference black hole with mass M s = 3 solar masses (or radius R s = 8.89 km) and temperature T s = 10 12 K. Using Equations (30) and (31) to relate the temperatures T b and T to the radius R, we can numerically solve Equation (33) and find the entropy of a spacetime or black hole as a function of its radius or mass.

For a star-like or supermassive black hole, we have T p ≪ T and T = T s ( R s / R ) 3 / 4 as seen from Equation (26). Further using the Mach-Schwarzschild M-R relation Equation (1), we have T = T s [ R s c 2 / ( 2 G M ) ] 3 / 4 . Then, the entropy of a star-like or supermassive black hole can be obtained by the following,

S B H = ∫ 0 M c 2 T d M = 4 c 2 7 T s ( 2 G R s c 2 ) 3 / 4 M 7 / 4 (34)

It is seen that the entropy of a star-like or supermassive black hole is proportional to the mass or radius according to S B H ∝ M 7 / 4 or S B H ∝ R 7 / 4 . ^{50} J/K. In

S s t a r = k B N p { l n [ V s t a r N p ( 2 π k B m p T s t a r h 2 ) 3 / 2 ] + 5 2 } ~ 18 k B N p (35)

where N p is the number density of proton in the star, m p is the mass of proton, V s t a r is the volume of the star.

From

black hole with the same mass, the entropy increases to 10^{37} J/K from 10^{36} J/K. If the black hole formed has only 5 solar masses by a supernova explosion, the entropy decreases to 10^{35} J/K from 10^{36} J/K because the supernova explosion has brought a significant amount of entropy away. The entropy of a star with 50 solar masses has entropy of ~10^{37} J/K. When it forms a black hole with 10 solar masses, which has entropy of 7 × 10^{36} J/K, at the end of its life after supernova explosion, the supernova explosion carries about 3 × 10^{36} J/K or more entropy away.

Conventionally, the entropy of a black hole is calculated according to the Hawking radiation. Considering the quantum effect near the event horizon, Hawking [^{23}/M K and power of ~3.56 × 10^{32}/M^{2} W. Here M is the mass of black hole in kilograms. For a star-like or more massive black hole, both the temperature and power of the Hawking radiation are negligible small. In accordance with the temperature of Hawking radiation, the entropy of the black hole is obtained as 3 × 10^{−7} M^{2} J/K, which is about 10^{20} times greater than that of star with the same mass as well as that of a dynamic black hole.

Now, we come back to Equation (33), to plot, in ^{35} J/K to about 10^{70} J/K. The entropy of the present highly ordered universe is still keeping quickly growing. Since the black hole universe is not an isolated system, its entropy is mostly coming from the mother universe due to accretions of matter and radiation. This increase does not lose the order significantly. This explains why the present universe, although it fully grows with temperature less than 3 K, is still highly ordered.

The black hole universe is not an isolated spacetime with k = 1 [

As a summary, the author has examined and overviewed thoroughly the new black hole universe model and completely described its development from the three fundamentals and its creative explanations to the existing observations of the universe. From this comprehensive investigation of this new cosmological model, the author has further revealed the fundamental regularities and laws of the black hole universe with respect to the spacetime origin, structure, evolution, equilibrium, expansion, acceleration, radiation energy, and entropy variation. These efforts will help us to uncover various regularities and mysteries of the universe. The results indicate that, standing on 1) the principle of spacetime black hole equivalence, 2) the cosmological principle of spacetime isotropy and homogeneity, and 3) the Einsteinian general theory of relativity, the black hole universe model can self-consistently describe the origin, structure, evolution, expansion, and acceleration of the universe, quantitatively explain the measurements of cosmic microwave background radiation, type Ia supernovae’s luminosity distance and redshift, and dynamic properties of star-like, massive, and supermassive black holes such as gamma-ray bursts, X-rays flares from galactic centers, and quasars, and fully overcome the difficulties of the conventional model of the universe such as the problems of horizon, flatness, monopole, inflation, dark matter, dark energy, and so on.

The black hole universe is ruled by one theory of spacetime (i.e. the Einsteinian general theory of relativity), based on two principles of spacetime (i.e. the principle of spacetime black hole equivalence and the cosmological principle of spacetime isotropy and homogeneity), regulated with five laws of spacetime (i.e. the conversion of spactieme mass-radius ratio, the equilibrium of static spacetime, the expansion and acceleration of dynamic spacetime, the conservation of childish spacetime radiation energy, and the entropy increase of spacetime). It is governed by the Friedmann equation that can be derived from Einstein’s general theory of relativity, with the FLRW metric that can be derived from the cosmological principle, the Mach-Schwarzschild mass-radius ratio, and the positive curvature of 3D space that can be obtained from the principle of spacetime black hole equivalence. Mathematically, the black hole universe is slightly different from the big bang universe (one has mass-radius ratio constant and k = 1, while another has mass constant and k = 0), but physically they are completely different.

The work that was done previously and involves partially with students was supported by the NSF/REU (Grant #: PHY-1263253 and PHY-1559870) at Alabama A & M University. The author is also thankful to the University’s Title III Program for travel support of his attending conferences.

The authors declare no conflicts of interest regarding the publication of this paper.

Zhang, T.X. (2018) The Principles and Laws of Black Hole Universe. Journal of Modern Physics, 9, 1838-1865. https://doi.org/10.4236/jmp.2018.99117