We live in a black hole. The accelerated expansion of the universe and dark energy are evidence that we live in a black hole!

[icarus2]

We live inside a black hole. I assert that the accelerated expansion of the universe and the dark energy effect are evidence that we live inside a black hole. Therefore, I claim that by verifying the dark energy term, we can prove that we live inside a black hole.

You may think that the Hubble-Lemaitre expansion of the universe conflicts with the Black Hole Cosmology, but before you make a definitive judgment on this, let's hear a little more!

1.The size of the event horizon based on the total mass of the observable universe

R_obs=46.5GLY
ρ_c=8.64x10^-27kgm^-3
R_S=2GM/c^2=491.6GLY

The size of the event horizon created by the total mass distribution of the observable universe is 491.6 GLY. The event horizon created by the total mass of the observable universe is roughly 10 times larger than the observable universe. Therefore, the observable universe exists inside the event horizon of a black hole created by its own mass.

There are several fatal weaknesses in this black hole cosmology.


2.Weaknesses of the Black Hole Cosmology

1) In a black hole, all matter is compressed into a singularity, so there is no space for humans to live. There is no almost flat space-time that could contain the observable universe inside a black hole.

2) In the black hole, singularity exist in the future, and in the universe, singularity exist in the past. Black hole and the universe are opposites.

3) The universe is expanding. Inside a black hole, all matter must contract to a singularity. The two models show opposite phenomena. It is difficult to explain the expansion of the universe inside a black hole. In addition, the universe is expanding at an accelerated rate.

Problems such as strong tidal force enough to disintegrate people, the movement of all matter in the direction of the singularity, and the expanding universe have been pointed out as fatal weaknesses of the Black Hole Cosmology. If our universe was a black hole, all galaxies should have collapsed into a singularity or exhibit motion in the direction of the singularity, but the real universe does not exhibit such motion characteristics. Therefore, the Black Hole Cosmology was judged to be inconsistent with the current observations, and the Black Hole Cosmology did not become a mainstream cosmological model.

Although this objection (or Weaknesses) appears to be clear and well-grounded, in fact, this objection also has its own fatal weaknesses.

Most physicists and astronomers believe that the singularity problem will be solved by quantum mechanics or some other unknown method. In other words, most scientists think that singularities don't exist. They are using it as a basis for criticism, even though they think that singularity will not exist.

We think that the singularity problem will ultimately be solved by some mechanism. Therefore, in the process of solving the singularity problem, there is a possibility that the singularity problem of the Black Hole Cosmology will also be solved.

For the singularity to disappear, there must be a repulsive force inside the black hole. Due to this repulsive force, an uncompressed region inevitably exists inside the black hole.

The remaining question is, 'Can the uncompressed region be larger than the observable universe?'

If the singularity disappears due to quantum mechanics, the uncompressed region will be very small compared to the observable universe.
But what if the singularity disappears by some other means than quantum mechanics?

3.Solutions to the problems of Black Hole Cosmology
Weakness: 3.1. In a black hole, all matter is compressed into a singularity, so there is no space for humans to live. There is no almost flat space-time that could contain the observable universe inside a black hole

Solution :
3.1.1.Mass defect effect due to gravitational binding energy or gravitational potential energy

● ----- r ----- ●

When two masses m are separated by r, the total energy of the system is

E_T = 2mc^2 - Gmm/r

If we introduce the negative equivalent mass "-m_gp" for the gravitational potential energy,

The total mass or equivalent mass m^* of the system is less than the mass of 2m when the two objects were in a free state. The bound objects experience a mass loss (defect) due to the gravitational binding energy. This is equivalent to having a negative equivalent mass in the system.


The concept of gravitational self-energy(U_gs) is the total of gravitational potential energy possessed by a certain object M itself. Since a certain object M itself is a binding state of infinitesimal mass dMs, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these. M = ΣdM. The gravitational self-energy is equal to the minus sign of the gravitational binding energy. Only the sign is different because it defines the gravitational binding energy as the energy that must be supplied to the system to bring the bound object into a free state.

U_gs=-(3/5)(GM^2)/R

In the case of a spherical uniform distribution, the total energy of the system, including gravitational potential energy, is

In the general case, the value of total gravitational potential energy (gravitational self-energy) is small enough to be negligible, compared to mass energy Mc^2. So generally, there was no need to consider gravitational potential energy. In the case of the Earth, the negative gravitational potential energy is -4.17x10^-10 of the Earth's mass energy, and in the case of the Sun, the negative gravitational potential energy is -1.27x10^-4 of the Sun's mass energy.

However, as R gets smaller, the absolute value of U_gs increases. For this reason, we can see that U_gs is likely to offset the mass energy in a certain radius. The mass defect effect due to binding energy has already been demonstrated in particle physics.

Thus, looking for the size in which gravitational self-energy becomes equal to rest mass energy by comparing both,

This equation means that if mass M is uniformly distributed within the radius R_gs, (negative) gravitational self-energy for such an object equals (positive) mass energy in size. So, for such an object, the (positive) mass energy and the (negative) gravitational self-energy are completely offset, and the total energy becomes zero. Since total energy of such an object is 0, gravity exercised on another object outside is also 0.

Comparing R_gs with R_S, the radius of Schwarzschild black hole,

This means that there exists the point where gravitational self-energy (- gravitational binding energy) becomes equal to mass energy within the radius of black hole, and that, supposing a uniform distribution, the value exists at the point 0.3R_S, about 30% level of the black hole radius. When applying the Viral theorem, this value is halved. R_gs-vir=0.15R_S.

The area of within R_gs has gravitational self-energy(gravitational potential energy) of negative value, which is larger than mass energy of positive value.

If r (radius of mass distribution) is less than R_gs, this area becomes negative energy (mass) state. There is a repulsive gravitational effect between the negative masses, which causes it to expand again.

From the equation above, even if some particle comes into the radius of black hole, it is not a fact that it contracts itself infinitely to the point R = 0. From the point R_gs, gravity is 0, and when it enters into the area of R_gs, total energy within R_gs region corresponds to negative values enabling anti-gravity to exist. This R_gs region comes to exert repulsive effects of gravity on the particles outside of it, therefore it interrupting the formation of singularity at the near the area R = 0

* When calculating the binding energy from general relativity, there is a slight difference in the R_gs value. It is about 2 times larger than the Newtonian calculation value. The basic mechanism and the core argument are the same.


R_{gp-GR} = 1.93R_gs = 1.16GM/c^2 = 0.58R_S


#Problems and Solutions of Black Hole Cosmology
https://www.researchgate.net/publication/359192496

#Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field
https://www.researchgate.net/publication/360096238

#Solution of the Singularity Problem of Black Hole
https://www.researchgate.net/publication/313314666

 

[icarus2]

If you have only the concept of positive energy, please refer to the following explanation.

The total energy of the system, including gravitational potential energy, is

From the point of view of mass defect, r=R_gs is the point where the total energy of the system is zero. For the system to compress more than this point, there must be an positive energy release from the system. However, since the total energy of the system is zero, there is no positive energy that the system can release. Therefore, the system cannot be more compressed than r=R_gs. So black hole doesn't have singularity. At this time, the emitted energy does not go out of the black hole. This energy is distributed in the R_gs < r ≤ R_S region.

In case of the smallest stellar black hole with three times the solar mass, R_S = 9km. R_gs of this object is as far as 3km. In other words, even in a black hole with smallest size that is made by the gravitational contraction of a star, the distribution of internal mass can’t be reduced below radius 3km. Before reaching the quantum mechanical scale, the singularity problem is solved by gravity itself.

When we generally consider the gravitational action due to the mass M of an object, M is not the mass of the particles that make up M in a free state, but the total mass or equivalent mass that reflects the negative binding energy. Therefore, this is consistent with the current gravitational model. In addition, since the point where the equivalent mass m^* switches to a negative mass state exists inside the black hole, it does not conflict with the observation results. In doing so, it solves the singularity problem of black holes.

3.1.2. Internal structure of a black hole according to this model



Fig.1.The internal structure of a black hole based on the radius of the mass (or energy) distribution
a) Existing Model. b) New Model. The area of within R_gs (or R_gs-vir) has gravitational potential energy (gravitational self-energy) of negative value, which is larger than mass energy of positive value. If r is less than R_gs, this area becomes negative energy (mass) state. There is a repulsive gravitational effect between the negative masses, which causes it to expand again. This area (within R_gs) exercises anti-gravity on all particles entering this area, and accordingly prevents all masses from gathering to r=0. Therefore the distribution of mass (energy) can't be reduced to at least radius R_gs. If, over time, the black hole stabilizes, the black hole does not have a singularity in the center, but it has a zero (total) energy zone. Since there is a repulsive gravitational effect between negative energies (masses), the mass distribution expands, and when the mass distribution expands, the magnitude of the negative gravitational self-energy decreases, so it enters the positive energy state again. When the system (mass distribution) becomes a positive energy state, gravitational contraction will exist again. In this way, gravitational contraction and expansion will be repeated until the total energy of the system becomes 0, and finally it will stabilize at a state where the total energy is 0.

3.1.3. Inside a sufficiently large black hole, there is enough space for intelligent life to exist
A black hole has no singularity, has a Zero Energy Zone with a total energy of zero, and this region is very large, reaching 15% ~ 30% of the radius of the black hole. It suggests an internal structure of a black hole that is completely different from the existing model. Inside the huge black hole, there is an area where intelligent life can live.

For example, if the masses are distributed approximately 46.5GLY with the average density of the current universe, the size of the black hole created by this mass distribution will be 491.6GLY, and the size of the Zero Energy Zone will be approximately 73.7GLY ~147.5GLY.
In other words, there is no strong tidal force and a region with almost flat space-time that can form a stable galaxy structure is much larger than the observable range of 46.5 GLY. The entire universe is estimated to be much larger than the observable universe, so it may not be at all unusual for us to observe only the Zero Energy Zone (nearly flat space-time).

*Taking general relativistic corrections into account, the Zero Energy Zone can be approximately 1.93 times larger. About 282.7GLY

Weakness: 3.2. In the black hole, singularity exist in the future, and in the universe, singularity exist in the past. Black hole and the universe are opposites

Solution :
Just because a singularity exists in the future in a black hole and a singularity in the universe in the past does not negate the Black Hole Cosmology. In a stellar black hole, an object enters the black hole from the event horizon, and in the case of the universe, it is only a case of expanding from a singularity toward the event horizon. It is still a phenomenon that occurs inside a universe black hole.

When an object is thrown upwards in Earth's gravitational field, it looks different when it rises up and when it comes down from its apex, but both events are just two aspects of a single event in the same gravitational field.

 

[icarus2]

Weakness: 3.3. The problem of cosmic expansion inside a black hole. The universe is expanding. It is difficult to explain the distance between galaxies inside a black hole. In addition, the universe is expanding at an accelerated rate.

Solution :
The size of the observable universe is 46.5 GLY, and the R_gs point created by this mass distribution is 147.5 GLY (GR ~ 282.7GLY). That is, we exist in a region where negative gravitational potential energy is greater than positive mass energy. To put it another way, we are in a region where repulsive forces dominate and we are experiencing accelerated expansion.
This is a characteristic consistent with the accelerated expansion effect of the universe caused by dark energy.

So, does the current standard cosmology contain these characteristics? Yes!

3.3.1. The logic behind the success of the standard cosmology

Matter:4.9% / Dark matter:26.8% / Dark energy : 68.3%
Let's look at the equation expressing (ρ+3P) as the critical density of the universe.

In the second Friedmann equation,
(1/R)(d^2R/dt^2) = -(4πG/3)(ρ+3P)

Matter + Dark Matter (approximately 31.7%) = ρ_m ~ (1/3)ρ_c
Dark energy density (approximately 68.3%) = ρ_Λ ~ (2/3)ρ_c
(Matter + Dark Matter)'s pressure = 3P_m ~ 0
Dark energy’s pressure = 3P_Λ = 3(-ρ_Λ) =3(-(2/3)ρ_c ) = -2ρ_c

ρ+3P≃ ρ_m +ρ_Λ +3(P_m +P_Λ)= (1/3)ρ_c +(2/3)ρ_c +3(−2/3)ρ_c= (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

ρ+3P ≃ (+1)ρ_c + (-2)ρ_c = (−1)ρ_c

The logic behind the success of standard cosmology is a universe with a positive mass density of (+1)ρ_c and a negative mass density of (-2)ρ_c. So, finally, the universe has a negative mass density of “(-1)ρ_c”, so accelerated expansion is taking place.

The current universe is similar to a state where the negative mass density is twice the positive mass density. And the total mass of the observable universe is the negative mass state.

3.3.2. The magnitude of negative gravitational potential energy and positive mass energy in the universe

If we find the Mass energy (Mc^2; M is the equivalent mass of positive energy.) and Gravitational potential energy (U_gp=(-M_gp)c^2; -M_gp is the equivalent mass of negative GPE) values at each range of gravitational interaction, Mass energy is an attractive component, and the gravitational potential energy (or gravitational self-energy) is a repulsive component. Critical density value p_c = 8.50 x 10^-27[kgm^-3] was used.

[Result summary]
At R=16.7Gly, U_gp = (-0.39)Mc^2

|U_gp| < (Mc^2) : Decelerating expansion period

At R=26.2Gly, U_gp = (-1.00)Mc^2

|U_gp| = (Mc^2) : Inflection point (About 5-7 billion years ago, consistent with standard cosmology.)

At R=46.5Gly, U_gp = (-3.08)Mc^2

|U_gp| > (Mc^2) : Accelerating expansion period

Since the universe is a combination of various substances (e.g. galaxies) and energies, gravitational binding energy, or gravitational potential energy, must be considered.
And, in fact, if we calculate the value, since negative gravitational potential energy is larger than positive mass energy, so the universe has accelerated expansion. The Gravitational Potential Energy Model describes decelerating expansion, inflection points, and accelerating expansion.

Since mass energy is proportional to M, whereas gravitational potential energy is proportional to -M^2/R, as mass increases, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.Therefore, as the universe ages and the range of gravitational interaction expands, a situation arises where the negative gravitational potential energy becomes greater than the positive mass energy, and thus the universe is accelerating expansion.

The acceleration equation can be derived through the Gravitational Potential Energy Model.

https://www.researchgate.net/publication/360096238

If we roughly calculate the value of the cosmological constant using the gravitational potential energy model,

Λ_gp = (6πGRρ/5c^2)^2 = 1.10 x 10^-52[m^-2]

This value is almost identical to the cosmological constant value obtained through the Planck satellite.

Λ_obs = 1.1056 x 10^-52[m^-2]

Dark energy is not a cosmological constant, it is a function of R(Radius of gravitational interaction) and ρ, and dark energy changes over time.

Gravitational potential energy 1) has been proven to exist due to the mass loss effect caused by binding energy, 2) satisfies the repulsive or anti-gravity requirement that leads to the accelerated expansion of the universe, 3) if you calculate its value numerically, it is larger than positive mass energy and can explain the dark energy density, 4) explains the inflection point where deceleration expansion changes to acceleration expansion, and 5) is also applied to solving the singularity problem of black holes.

4. How can we prove that Black Hole Cosmology is correct?
In this model, the source of dark energy is gravitational potential energy (or gravitational binding energy), which allows us to find an equation to describe dark energy. As a result, dark energy is not a cosmological constant, but rather a function of time.

Dark energy term obtained through the gravitational potential energy model :

(1/3)Λ(t)c^2 = 3(2πGR(t)ρ(t)/5c)^2

We can check the time dependence of the dark energy term through observation. Also, the inflection point where the universe changes from deceleration to acceleration is the point where the size of negative gravitational potential energy and positive mass energy become equal. This can be verified by calculating the inflection point and comparing it with the observation results.

Recently, several observational results have been published suggesting that dark energy may be a time-varying value.

1)The Dark Energy Survey team(2024.01)
The Dark Energy Survey team, an international collaborative team of more than 400 scientists, announced the results of an analysis of 1,499 supernovae. (2024.01)

This figure is approximately 30 times more than the 52 supernovae used by the team that reported the accelerated expansion of the universe in 1998.

https://noirlab.edu/public/news/noirlab2401/?lang

The standard cosmological model is known as ΛCDM, or ‘Lambda cold dark matter’. This mathematical model describes how the Universe evolves using just a few features such as the density of matter, the type of matter and the behavior of dark energy. While ΛCDM assumes the density of dark energy in the Universe is constant over cosmic time and doesn’t dilute as the Universe expands, the DES Supernova Survey results hint that this may not be true.

“There are tantalizing hints that dark energy changes with time,” said Davis, “We find that the simplest model of dark energy — ΛCDM — is not the best fit. It’s not so far off that we’ve ruled it out, but in the quest to understand what is accelerating the expansion of the Universe this is an intriguing new piece of the puzzle. A more complex explanation might be needed.”

2)Dark Energy Spectroscopic Instrument team(2024.04 / 2024.11)

https://arstechnica.com/science/2024/04/dark-energy-might-not-be-constant-after-all/#gsc.tab=0

"It's not yet a clear confirmation, but the best fit is actually with a time-varying dark energy," said Palanque-Delabrouille of the results. "What's interesting is that it's consistent over the first three points. The dashed curve [see graph above] is our best fit, and that corresponds to a model where dark energy is not a simple constant nor a simple Lambda CDM dark energy but a dark energy component that would vary with time.

The possibility that dark energy density varies over time has been raised, but the interpretation of the observation results is still in its early stages, so it will take several more years to make a final judgment.

I think that the accelerated expansion of the universe and the dark energy effect are evidence that we live inside a black hole. Therefore, I claim that by verifying the dark energy term, we can prove that we live inside a black hole.

I have provided a means to verify the model by presenting the core idea, dark energy term, and method to obtain the inflection point. However, due to my limited knowledge, results beyond these will require someone better than me.


#Problems and Solutions of Black Hole Cosmology
https://www.researchgate.net/publication/359192496

#Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field
https://www.researchgate.net/publication/360096238

#Solution of the Singularity Problem of Black Hole
https://www.researchgate.net/publication/313314666