# Dark energy is gravitational self-energy or the gravitational action of the gravitational field

#### 7icarus7

The source of dark energy is gravitational self-energy or the gravitational action of the gravitational field!

1. Gravitational potential energy is negative energy

1) Alan Guth said
The energy of a gravitational field is negative!
The positive energy of the false vacuum was compensated by the negative energy of gravity.

2) Stephen Hawking also said
The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

Both said that gravitational potential energy is negative energy and is the true energy that can cancel positive mass energy.

3) Negative energy (mass) density in standard cosmology
From the second Friedmann equation or acceleration equation,

(1/R)(d^2R/dt^2)=-(4πG/3)(ρ+3P)

In standard cosmology, it is explained by introducing an entity that has a positive mass density but exerts a negative pressure.

p + 3P = p + 3(-p) = - 2p

However, If we rearrange the dark energy term, the final result is a negative mass density of -2p.
In the standard cosmology, accelerated expansion is impossible without negative mass density. It is just that the negative mass density term is called negative pressure, so it is not recognized.

4) Gravitational binding energy and mass defect
https://en.wikipedia.org/wiki/Gravitational binding energy
Two bodies, placed at the distance R from each other and reciprocally not moving, exert a gravitational force on a third body slightly smaller when R is small. This can be seen as a negative mass component of the system, equal, for uniformly spherical solutions, to: 5) Since gravitational self-energy is proportional to -M^2/R, The greater the mass, the greater the gravitational self-energy ratio
In the dimensional analysis of energy, E has kg(m/s)^2, so all energy can be expressed in the form of (mass) x (speed)^2. So, E=Mc^2 holds true for all kinds of energy. "-M_gs" is the equivalent mass of gravitational self-energy. It is a negative equivalent mass term.

Earth's -M_gs = (- 4.17x10^-10)M_Earth
Sun's -M_gs = (- 1.27x10^-4)M_Sun
Black hole's -M_gs = (- 0.3)M_Black-hole

For example, in the case of a black hole,
-M_gs=-(3/5)(GM^2)/(Rc^2)=-(3/5)(GM^2)/((2GM/c^2)c^2)=-(3/10)M=-0.3M_Black-hole

What about the universe with more mass?

2. In the universe, if we calculate the gravitational self-energy or total gravitational potential energy
The universe is almost flat, and its mass density is also very low. Thus, Newtonian mechanics approximation can be applied.
Since the particle horizon is the range of interaction, if we find the Mass energy (Mc^2) and Gravitational self-energy ((-M_gs)c^2) values at each particle horizon, Mass energy is an attractive component, and the equivalent mass of gravitational self-energy is a repulsive component. Critical density value p_c = 8.50 x 10^-27[kgm^-3] was used.

At particle horizon R=16.7Gly, (-M_gs)c^2 = (-0.39M)c^2 : |(-M_gs)c^2| < (Mc^2) : Decelerated expansion period
At particle horizon R=26.2Gly, (-M_gs)c^2 = (-1.00M)c^2 : |(-M_gs)c^2| = (Mc^2) : Inflection point (About 5-7 billion years ago, consistent with standard cosmology.)
At particle horizon R=46.5Gly, (-M_gs)c^2 = (-3.04M)c^2 : |(-M_gs)c^2| > (Mc^2) : Accelerated expansion period

Even in the universe, gravitational potential energy (or gravitational action of the gravitational field) must be considered.
And, in fact, if we calculate the value, since gravitational self-energy is larger than mass energy, so the universe has accelerated expansion.
Gravitational self-energy accounts for decelerated expansion, inflection point, and accelerated expansion.

3. New Friedmann's equations and the dark energy term from the gravitational self-energy model   Finding the dark energy term with this model is similar to the standard cosmology value.
Gravitational potential energy is a concept that has already existed, and does not assume a bizarre existence that has a positive inertial mass and exerts a negative pressure. There are no problems like fine tuning or CCC problem.

In standard cosmology, the energy density of dark energy is a constant. However, in the gravitational self-energy model, dark energy density is a variable.
The dark energy (or cosmological constant term) is a function of time. Thus, this model can be verified.

# Dark energy is the Gravitational Potential Energy or Gravitational Self-Energy
https://www.researchgate.net/publication/360096238

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#### 7icarus7

*Background description
Why do we need gravitational potential energy or gravitational field energy?
1) The fundamental principle of general relativity states that “all energy is a source of gravity”. However, the field equation created by Einstein did not fully realize this principle

The energy of the gravitational field must also function as a gravitational source.
Einstein was also aware of this, and for over two years, beginning in 1913, he worked to formulate a field equation that included the energy-momentum of the gravitational field. However, because it was difficult to define the energy of the gravitational field in general relativity, Einstein could not complete the field equation including the gravitational action of the gravitational field.
So, the singularity problem and the dark energy problem came into existence.

2) As the mass increases, the ratio of negative gravitational potential energy to mass energy increases
-M_gs = Equivalent mass of total gravitational potential energy (gravitational self energy) of an object
Earth's -M_gs = (- 4.17 x 10^-10)M_Earth
Sun's -M_gs = (- 1.27 x 10^-4)M_Sun
Black hole's -M_gs = (- 3 x 10^-1)M_Black-hole
What about the universe with more mass?

1. Gravitation and Spacetime (Book) : 25~29P Different forms of energy as source of gravity : Gravitational energy in Earth

If we want to discover whether gravity gravitates, we must examine the behavior of large masses,of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6×10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.

2. Explanation of GRAVITY PROBE B team
Do gravitational fields produce their own gravity?

A gravitational field contains energy just like electromagnetic fields do. This energy also produces its own gravity, and this means that unlike all other fields, gravity can interact with itself and is not 'neutral'. The energy locked up in the gravitational field of the earth is about equal to the mass of Mount Everest, so that for most applications, you do not have to worry about this 'self-interaction' of gravity when you calculate how other bodies move in the earth's gravitational field.

3. Wikipedia, Gravitational binding energy
Two bodies, placed at the distance R from each other and reciprocally not moving, exert a gravitational force on a third body slightly smaller when R is small. This can be seen as a negative mass component of the system, equal, for uniformly spherical solutions, to:

M_binding=-(3/5)(GM^2)/(Rc^2)

For example, the fact that Earth is a gravitationally-bound sphere of its current size costs 2.49421×1015 kg of mass (roughly one fourth the mass of Phobos – see above for the same value in Joules), and if its atoms were sparse over an arbitrarily large volume the Earth would weigh its current mass plus 2.49421×1015 kg kilograms (and its gravitational pull over a third body would be accordingly stronger).

4. Gravitation and Spacetime (Book)
In writing the field equation (48) we have assumed that the quantity T^{\mu \nu } is the energy-momentum tensor of matter. In order to obtain a linear field equation we have left out the effect of the gravitational field upon itself. Because of this omission, our linear field equation has several (related) defects:

(1) According to (48) matter acts on the gravitational field (changes the fields), but there is no mutual action of gravitational fields on matter; that is, the gravitational field can acquire energy-momentum from matter, but nevertheless the energy-momentum of matter is conserved ({\partial _\nu }{T^{\mu \nu }} = 0). This is an inconsistency.
(2) Gravitational energy does not act as source of gravitation, in contradiction to the principle of equivalence. Thus, although Eq. (48) may be a fair approximation in the case of weak gravitational fields, it cannot be an exact equation.
The obvious way to correct for our sin of omission is to include the energy-momentum tensor of the gravitational field in T^{\mu \nu }. This means that we take for the quantity T^{\mu \nu } the total energy-momentum tensor of matter plus gravitation:

T^{\mu \nu }} = T_{(m)}^{\mu \nu } + {t^{\mu \nu }}

5. Problem with Einstein's field equation

The basis of modern cosmology is Einstein's 1915 field equation. However, this field equation has a singularity problem inside the black hole. In other words, the field equation created by Einstein is likely to be incomplete.

The fundamental principle of general relativity states that “all energy is a source of gravity”. However, the field equation created by Einstein did not fully realize this principle.

The energy of the gravitational field must also function as a gravitational source.
Einstein was also aware of this, and for over two years, beginning in 1913, he worked to formulate a field equation that included the energy of the gravitational field. However, because it was difficult to define the energy of the gravitational field in general relativity, Einstein could not complete the field equation including the gravitational action of the gravitational field. So, without the energy-momentum tensor of the gravitational field, the 1915 field equation came out.

Because it was difficult to define the energy-momentum tensor of the gravitational field in general relativity, in this paper, based on the corresponding principle that general relativity is approximated by Newtonian mechanics in a weak field, I approach the gravitational action of the gravitational field as an approximate way. And I prove that this method suggests sufficiently meaningful results in cosmology.

There are Landau–Lifshitz pseudotensor and Einstein pseudotensor methods for describing the energy-momentum of the gravitational field, but it does not seem to have formed a consensus among all people yet. In addition, it seems that solution of singularity through these pseudo-tensor methods or cosmological application methods have not yet been proposed. As described in this paper, the energy of the gravitational field is likely a source of dark energy, so if you can, try it from these pseudo-tensors or from a new field equation with the energy-momentum tensor of the gravitational field.

#Dark Energy is Gravitational Potential Energy or Gravitational Self Energy
#On the solution of the strong gravitational field the solution of the Singularity problem the origin of Dark energy and Dark matter

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#### 7icarus7

Most of the people who read this article will have a strong objection and antipathy to the negative mass (density), but~

1.The first result of Friedmann's equation for accelerated expansion was negative mass density

Nobel lecture by Adam Riess : The official website of the Nobel Prize
Refer to time 11m : 35s ~
https://www.nobelprize.org/mediaplayer/?id=1729

=====
Negative Mass?
Actually the first indication of the discovery!

=====

HSS(The High-z Supernova Search) team : if Λ=0, Ω_m = - 0.38(±0.22) : negative mass density
SCP(Supernova Cosmology Project) team : if Λ=0, Ω_m = - 0.4(±0.1) : negative mass density

They had negative thoughts about negative mass. So, they discarded the negative mass (density) without sufficient scientific review. They corrected the equation and argued that the accelerated expansion of the universe was evidence of the existence of a cosmological constant.

They introduce negative pressure, which hides the negative mass density in the negative pressure, but this does not mean that the negative mass density has disappeared, it has only lessened the antipathy of people by the name change. It cannot change the essence.

ρ_Λ + 3P_Λ = ρ_Λ + 3(-ρ_Λ) = - 2ρ_Λ

If we rearrange the dark energy term, the final result is a negative mass density of -2ρ_Λ.
In the standard cosmology, accelerated expansion is impossible without negative mass density.

2.Logical structure of the standard cosmology
You need to look at the logical structure of standard cosmology.
Let's look at the expression expressing (ρ+3P) as the critical density of the universe.

(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 = P_m ~ 0
Dark energy’s pressure =3P_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 = (ρ_c) + (-2ρ_c) = −ρ_c

ρ+3P
≃ (+1ρ_c) + (-2ρ_c) = −1ρ_c

Standard cosmology is a universe with a positive mass density of +1ρ_c and a negative mass density of -2ρ_c. So, finally, the universe has a negative mass density of “- ρ_c”, so accelerated expansion is taking place.

However, many people say that the accelerated expansion is explained by negative pressure, and there is no such thing as negative mass (density).

Because there is preconceived notion about negative mass. So, they talk only to negative pressure, and stop explaining.

The gravitational potential energy model is a model with a positive mass density of +1ρ_c and a gravitational potential energy (binding energy) of -2ρ_c.

In the generality of cases, the value of gravitational potential energy is small enough to be negligible, compared to mass energy Mc^2. However, as more mass is collected, the ratio of (negative) gravitational potential energy to (positive) mass energy increases.

In the case of Moon,
U_{gs - Moon} = ( - 1.89 x 10^ -11)M_{Moon}(c^2)
In the case of Earth,
U_{gs - Earth} = ( - 4.17 x 10^ -10)M_{Earth}(c^2)
In the case of the Sun,
U_{gs - Sun}} = ( - 1.27 x 10^ -4)(M_{Sun}(c^2)
In case of a Black hole,
U_{gs - Black - hole} = ( - 3.00 x 10^-1){M_{Black - hole}(c^2)

And, in the case of a universe with a larger mass,

Mc^2 = | - (3/5)(GM^2)/R_gs |
R_gs = sqrt (5c^2/4πGρ) ~ 18.7Gly ~ 26.2Gly (Depends on average density value)

When the particle horizon was less than approximately 18.7Gly ~ 26.2Gly, the universe had a decelerated expansion, and as the particle horizon became larger than approximately 18.7Gly ~ 26.2Gly, the universe began to undergo accelerated expansion. This inflection point is approximately 7 to 5 billion years ago.

Since mass energy is proportional to M, whereas gravitational self-energy is proportional to -M^2/R, as mass increases, the ratio of (negative) gravitational self-energy to (positive) mass energy increases.
Therefore, as the universe ages and the particle horizon expands, the phenomenon of changing from decelerated expansion to accelerated expansion occurs.

Please don't argue with negative mass density (don't think about whether it exists or not), shut up and it's time to calculate. Already, the accelerating expansion of the universe has become an important issue because it is a phenomenon contrary to the prevailing predictions of the mainstream. The mainstream was also wrong in its predictions about the rotation curve of galaxies. Dark Energy Problem and Dark Matter Problem.
One of the lessons of relativity and quantum mechanics is that we don't judge nature by the logic we learn in our daily lives.

Mass defect due to binding energy is a proven physics, and the formula says that on a cosmic scale, the size can also be greater than the mass energy.

I'm presenting the dark energy term as a function of time, so I'd appreciate a serious review of the model by people better than me.

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