About the Solution of the Singularity Problem of Black Hole

[icarus2]

I apologize for my poor English.

 

[ About the Solution of the Singularity Problem of Black Hole ]

 

1. Understanding of the problem : Generation of singularity

Generally, stars are under gravitational contraction by their own gravity and it is known that if this is contracted within a certain radius (like Schwarzschild radius), it makes a black hole which even lights cannot escape from.

Since gravity is generally an attractive force, gravitational contraction continues to exist in the black hole, too. Thus, in the central part of black hole exists an area with infinite density of energy, which point we call singularity.

Such singularity denies application of the existing laws of physics and it is unnatural for a certain substantial object to have infinite density of energy. Besides, such singularity has never been observed as substance but is just a mathematical result of general relativity, which is considered a defect or limit of the theory.

 

We assume that the solution for this singularity consists in quantum mechanics. Though exact explanation is not available because quantum gravity theory in integration of quantum mechanics and gravity has not been completed yet.

 

This writing will prove that an object of positive energy has the minimum size for its existence and that since this size is in proportion to that of energy, there is no singularity with infinite density.

 

 

2. Solution of the problem

 

2-1. Gravitational potential energy with negative values.

 

~~~~~~~~~~

 

2-1-3. U( r) = - GMm/r (except r=0) is considered to provide consequently the right explanation for all points.

Teachers and professors have explained that it is alright to set the randomly reference point for gravitational potential energy because, since the variation of gravitational potential energy has caused kinetic change in the problem under review, there was no problem in dealing with only the variation of gravitational potential energy.

 

From the equation K + U = const. we obtain such equation as [math]\Delta K = - \Delta U[/math], which can explain motion with variation, but this neither means that all observers in the same inertial system may set randomly reference point at random nor confirms that U is an object with an optional value.

 

Let's consider the following case that the value of gravitational potential energy has been fixed for the distance of 0 to infinity from gravitational source.

 

 

Even though, as above, gravitational potential energy has the value of energy defined for r= 0 to r= infinity from gravitational source, we can obtain the right result in a problem in which its variation matters.

 

2-1-4. Effect of mass defect in atomic scale caused by binding energy

 

~~~~~~~~~

 

2-2. Gravitational self-energy or Gravitational binding energy

The concept of gravitational self-energy 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 dM, it involves the existence of gravitational potential energy among these dMs and is the value of adding up these.

 

[math]M = \sum {dM} [/math]

Fig06. Since all mass M is a set of infinitesimal mass dMs and each dM is gravitational source, too, there exists gravitational potential energy among each of dMs. Generally, gravitational potential energy by infinitesimal mass that consists of an object itself is reflected on the mass of the object itself. Mass of an object measured from its outside corresponds to the value of dividing the total of all energy into c^2.

 

Gravitational self-energy or Gravitational binding energy([math]-U_{gs}[/math]) in case of uniform density is given by:

 

[math]{U_{gs}} = - \frac{3}{5}\frac{{G{M^2}}}{R}[/math]

([math]{U_{gs}}[/math] : gravitational self-energy)

 

2-3. For black hole or singularity, never fail to consider gravitational self-energy

In the generality of cases, the value of gravitational self-energy is small enough to be negligible, compared to mass energy mc^2.

 

Therefore, in usual cases, [math]|{U_{gs}}| < < M{c^2}[/math], so generally, there was no need to consider gravitational self-energy.

 

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

This equation means that if infinitesimal mass is uniformly distributed within the radius R_{gs}, gravitational self-energy for such an object equals mass energy in size. So, in case of such an object, mass energy and gravitational self-energy can be completely offset while total energy is zero. Since total energy of such an object is 0, gravity exercised on another object outside is also 0.

 

Comparing [math]R_{gs}[/math] with [math]R_B(=R_S)[/math], the radius of Schwarzschild black hole,

 

This means that there exists the point where gravitational self-energy becomes equal to mass energy within the radius of black hole, and that, supposing a uniform distribution, the value exists at the point [math]0.3R_{B}[/math], a 30% level of the black hole radius.

Even with kinetic energy and virial theorem applied only the radius diminishes as negative energy counterbalances positive energy, but no effects at all on this point: “there is a zone which cannot be compressed anymore due to the negative gravitational potential energy”)

 

Since this value is on a level not negligible against the size of black hole, we should never fail to consider “gravitational self-energy" for case of black hole.

 

 

2-4. Black hole does not have a singularity and there exists a zone that has a uniform energy density within the black hole.

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 [math]R_{gs}[/math], gravity is 0, and when it enters into the area of [math]R_{gs}[/math], total energy within [math]R_{gs}[/math] region corresponds to negative values enabling antigravity to exist.

 

This [math]0.3R_{B}(0.3R_{S})[/math] 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.

 

Fig07. Considering gravitational potential energy for black hole, the area of within [math]R_{gs}[/math] has gravitational self-energy of negative value, which is larger than mass energy of positive value. This area(within [math]R_{gs}[/math]) exercises anti-gravity on all particles entering this area anew, and accordingly prevents all masses from gathering to r=0.

 

Antigravity effect by negative mass :

 

However, it still can perform the function as black hole because [math]R_{gs}[/math] is only 30% of [math]R_{B}[/math] with a large difference in volume and, comparing total mass, it still can correspond to a very large quantity of mass. Therefore, it still can perform the function as black hole on the objects outside of [math]R_{B}[/math].

 

 

2-5. The minimal size of existence

 

~~~~~~~~~~

 

2-6. Expansion of the general relativity

 

2-6-1. We can solve the problem of singularity by separating the term([math]- {M_{gs}} = \frac{{{U_{gs}}}}{{{c^2}}}[/math]) of gravitational self-energy from mass and including it in the solutions of field equation.

 

M --> [math]M + (-M_{gs})[/math]

 

In the Schwarzschild solution,

 

~~~~~~~~~

 

For Schwarzschild black hole, the Kretschmann scalar is,

 

It does not diverge. Therefore, black hole doesn't have singularity.

~~~~~~~~~~

 

 

* Waiting for quantum gravity theory to be completed to solve the singularity issue in a black hole is wrong as it was made by our stereotypes.

 

When there occurred a problem in singular “point”, one dimensional idea that problems should be solved from λ, wavelength that has a little bigger than “point” was partially acted. Of course, we should try to establish a quantum gravity theory for other reasons.

 

 

We can think of a black hole of big size and approach this problem by reducing the mass of this black hole. In other words, we should form a certain internal structure of usual size and apply the experience that we had applied the limit.

 

[math]\mathop {\lim }\limits_{M \to small} {R_{gs}}[/math]

 

If you are still uncomfortable with [math]R_{gs}[/math], think about a black hole with the size 10 billion times bigger than the solar mass. Schwarzschild radius of this black hole is [math]{R_S} = 3 \times {10^{10}}km[/math] and [math]R_{gs}[/math] of this black hole [math]1 \times {10^{10}}km[/math].

 

Average density of this black hole is about [math]{1.81kg/m^3}[/math]. However average density of the Earth is about [math]{5,200kg/m^3}[/math].

 

Is it a size that requires quantum mechanics? Is it a high density state that requires quantum mechanics? Black hole of this size is Newtonian mechanics’ object and therefore, gravitational potential energy must be considered.

 

Let's reduce the mass of this black hole gradually and approach three times the solar mass, the smallest size of black hole where stars can be formed!

 

In case of the smallest black hole with three times the solar mass, [math]{R_S} = 9km[/math]. [math]R_{gs}[/math] of this object is as far as 3km. In other words, even in a black hole with smallest size that is made by the contraction of a star, the distribution of internal mass can't be reduced to at least radius 3km([math]R_{gs}[/math]).

 

Black hole does not have a singularity and there exists a zone that has a uniform energy density.

 

==========

#Paper

On Problems and Solutions of General Relativity. (Commemoration of the 100th Anniversary of General Relativity)

https://www.researchgate.net/publication/287217009

Edited June 23, 2017 by icarus2

[beecee]

* Waiting for quantum gravity theory to be completed to solve the singularity issue in a black hole is wrong as it was made by our stereotypes.

OK, as a lay person, this is what I do know about BH's.....

[1]Once the Schwarzchild radius is reached for any mass, further collapse is compulsory......hence the BH aspect.

[2]Most scientists worth their salt, do not believe any point singularity exists, with infinite quantities such as spacetime curvature and density

[3] GR fails at the quantum/Planck level, so in essence we should be able to conclude based on GR success and incredible predictability, that the "compulsory collapse"mentioned in [1] should apply at least up to the quantum/Planck realm.

[4] Noting that probably point singularities do not exist, and accepting that collapse occurs at least up to the quantum/Planck level, we can imo, speculate a surface of sorts at or below that level, being obviously of incredible density and mass, and along with spacetime at those levels, possibly in some unknown form.

Edited June 23, 2017 by beecee

[Mordred]

Lets start with "define energy".

 

Energy "the ability to perform work". So negative energy would have less ability to perform work or action. Can you see the problem here ? in order to perform work you would need to add energy (sounds endothermic lol)

 

The only way negative energy makes any sense. Is if it is a positive value that is of negative value compared to a higher value. Or a change in vector sign under vector addition. However a change in vector sign is still positive energy/density.

 

In the above you are using negative energy in terms of negative mass.

 

Great now define mass " Resistance to inertia change " so define negative resistance to inertia change...see the problem?

 

(PS never ceases to amaze me, how often posters trying to develop a speculative model forget the definitions and meaning of the terms they are using).

 

Yes English isn't your first lanquage but these definitions are translated to your lanquage.

 

Using vector sign as a negative value is fine for charge flow. Works great for the electromagnetic field.

 

However gravity is always charge positive.

What you describe above amounts to some antigravity dynamic which simply does not exist.

 

Now in Cosmology we have negative pressure/vacuum to some baseline. That being the cosmological constant aka dark energy. However this still has a positive energy density value (the negative is a vector treatment).

 

The problem in the above is that your negative energy and negative mass terms are being used in the sense of antigravity. Which has never been observed or ever detected.

 

!

Moderator Note

this thread belongs in our speculation forum as it is a personal model. However as I am partaking in this discussion and its poor form to perform Moderator action on a thread your participating in. (Unless a clear rules violation). I will wait till another member of the Moderator staff moves it.

Edited June 23, 2017 by Mordred

[icarus2]

OK, as a lay person, this is what I do know about BH's.....

[1]Once the Schwarzchild radius is reached for any mass, further collapse is compulsory......hence the BH aspect.

[2]Most scientists worth their salt, do not believe any point singularity exists, with infinite quantities such as spacetime curvature and density

[3] GR fails at the quantum/Planck level, so in essence we should be able to conclude based on GR success and incredible predictability, that the "compulsory collapse"mentioned in [1] should apply at least up to the quantum/Planck realm.

[4] Noting that probably point singularities do not exist, and accepting that collapse occurs at least up to the quantum/Planck level, we can imo, speculate a surface of sorts at or below that level, being obviously of incredible density and mass, and along with spacetime at those levels, possibly in some unknown form.

 

I'm sorry! I can't speak English well.

"[1]Once the Schwarzchild radius is reached for any mass, further collapse is compulsory......hence the BH aspect." :

--> OK.

[2]Most scientists worth their salt, do not believe any point singularity exists, with infinite quantities such as spacetime curvature and density

--> Yes.

[3] GR fails at the quantum/Planck level,

--> Yes.

//so in essence we should be able to conclude based on GR success and incredible predictability, that the "compulsory collapse"mentioned in [1] should apply at least up to the quantum/Planck realm.//

--> No, because of that field equation of general relativity does not include the gravitational potential energy term. And IMO, gravitational contraction should stop at R_gs(0.3R_S, 0.3*event horizon).

Even in a black hole with smallest size that is made by the contraction of a star, the distribution of internal mass can't be reduced to at least radius 3km(). Therefore, they do not reach the planck scale.

.

[beecee]

 

I'm sorry! I can't speak English well.

 

 

"[1]Once the Schwarzchild radius is reached for any mass, further collapse is compulsory......hence the BH aspect." :

--> OK.

 

[2]Most scientists worth their salt, do not believe any point singularity exists, with infinite quantities such as spacetime curvature and density

--> Yes.

 

[3] GR fails at the quantum/Planck level,

--> Yes.

 

//so in essence we should be able to conclude based on GR success and incredible predictability, that the "compulsory collapse"mentioned in [1] should apply at least up to the quantum/Planck realm.//

--> No, because of that field equation of general relativity does not include the gravitational potential energy term. And IMO, gravitational contraction should stop at R_gs(0.3R_S, 0.3*event horizon).

 

Even in a black hole with smallest size that is made by the contraction of a star, the distribution of internal mass can't be reduced to at least radius 3km(). Therefore, they do not reach the planck scale.

.

You seem to have contradicted yourself somewhat there.....Understandable since english is not your first language.

You agreed with my point 1, and then you conclude in saying gravitational collapse should stop.

Irrespective, evidence supports what I said in point 1...Once the Schwarzchild radius is reached further collapse is "compulsory"

Plus the "Dying Pulse Train" effect as predisted by GR, also supports total collapse.

http://www.indiana.edu/~geol105/images/gaia_chapter_1/death_spiral.htm

Edited June 24, 2017 by beecee

[icarus2]

Lets start with "define energy".

 

Energy "the ability to perform work". So negative energy would have less ability to perform work or action. Can you see the problem here ? in order to perform work you would need to add energy (sounds endothermic lol)

 

The only way negative energy makes any sense. Is if it is a positive value that is of negative value compared to a higher value. Or a change in vector sign under vector addition. However a change in vector sign is still positive energy/density.

 

I apologize for my poor English.

 

The definition is for elementary school students. And, working is not a positive energy, but a change of energy.

In the gravitational field, U is negative, U = - GMm/r, ΔU = -ΔK

 

Edward Tryon, Stephen Hawking, Alan Guth, and Alexander Vilenkin are the pioneers who advocated that positive mass energy could be offset by gravitational potential energy.

 

Stephen Hawking’s book “A Brief History of Time” and

Alan Guth’s lecture : Inflationary Cosmology : about 4m:50s~

 

https://youtu.be/vG0_Y0MtjCM?t=289

=====

The energy of a gravitational field is negative!

 

The positive energy of the false vacuum was compensated by the negative energy of gravity. The total energy of the universe may very well be zero.

=====

 

Of course, the negative mass I claim is different from the gravitational potential energy. However, they treat negative gravitational potential energy as real energy that can offset positive mass energy.

 

In the above you are using negative energy in terms of negative mass.

 

Great now define mass " Resistance to inertia change " so define negative resistance to inertia change...see the problem?

 

(PS never ceases to amaze me, how often posters trying to develop a speculative model forget the definitions and meaning of the terms they are using).

 

 

Not everyone thinks that it is a problem. And not everyone is shocked.

=====

http://www.telegraph.co.uk/science/2017/04/19/physicists-create-mind-bending-negative-mass-accelerates-backwards/

 

“Washington State University physicists explained that this mass, unlike every physical object in the world we know, accelerates backwards when pushed.”

~~~~~

Our everyday world sees only the positive effect of the law: if you push an object, it moves away from you.

 

“That’s what most things that we’re used to do,” said Michael Forbes, a WSU assistant professor of physics and astronomy and an affiliate assistant professor at the University of Washington. “With negative mass, if you push something, it accelerates toward you.”

 

~~~~~

 

The heightened control gives researchers a new tool to engineer experiments to study similar behaviours in astrophysics, such as neutron stars, and cosmological phenomena like black holes and dark energy, where experiments are impossible.

=====

 

Yes English isn't your first lanquage but these definitions are translated to your lanquage.

 

Using vector sign as a negative value is fine for charge flow. Works great for the electromagnetic field.

 

However gravity is always charge positive.

What you describe above amounts to some antigravity dynamic which simply does not exist.

 

Now in Cosmology we have negative pressure/vacuum to some baseline. That being the cosmological constant aka dark energy. However this still has a positive energy density value (the negative is a vector treatment).

 

The problem in the above is that your negative energy and negative mass terms are being used in the sense of antigravity. Which has never been observed or ever detected.

 

 

We do not know the origin of dark energy. Therefore, strictly speaking, it(something with positive energy density and negative pressure) is not a truth, but a model or an assumption.

 

In addition, (positive or negative) pressure is not the fundamental force. We know that there are four fundamental forces. So, origin of negative pressure is one of four fundamental force, or a new force. Therefore, anti-gravity is one of those candidates.

Edited June 25, 2017 by icarus2

[Mordred]

Why did you post references on what I am already aware of. I asked you to apply those basic definitions to your theory.

 

None of the above contradicts anything I've stated. I specifically used those examples to point out a key problem in how your post treats negative energy.

 

Actually your comments on the above links just tell me you don't understand how negative energy is applied to those articles.

 

in particular this comment.

. We know that there are four fundamental forces. So, origin of negative pressure is one of four fundamental force, or a new force. Therefore, anti-gravity is one of those candidates.

Every example you gave above has a positive energy value that under vector addition equates to negative energy in terms of pressure.

 

The positive energy for for the cosmological constant (dark energy) for example is [latex]7.2*10^{-10} joules/metre^3[/latex]

 

It is not a negative value, The negative pressure term arises from a specific formula called an equation of state.

 

[latex]w=\frac{p}{\rho}[/latex] where w=-1 for the cosmological constant.

 

Have you ever read the paper in the first link ? It applies a specific treatment for energy.

 

[latex]E_r=\frac{\hbar^2k^2_r}{2m}[/latex]

 

That paper is specifically describing variation of "effective mass" KEY WORD "Variation"

 

https://arxiv.org/abs/1612.04055

 

Would you like me to explain the pressure relations in Allen Guths work? you will find it relates back to the first relation I posted.

 

Let me ask you, Do you you understand the vector treatments on the three links you just provided?

 

Ie I assign contraction energy as a positive vector (positive pressure.) An expansion I describe as a negative vector aka negative pressure.

 

In electromagnetic under charge. I assign positive energy to positive charge which describes a direction of flow, negative flow of charge would be flow in the opposite direction. (charge is modelled as a vector)

 

Much like the first link you provided.

Edited June 25, 2017 by Mordred

[icarus2]

You seem to have contradicted yourself somewhat there.....

You agreed with my point 1, and then you conclude in saying gravitational collapse should stop.

 

 

At the Schwarzchild radius([math]R_S[/math]), gravitational collapse exists.

But, according to my research, gravitational collapse should be stopped at [math]R_{gs}[/math] ( [math]0.3R_{S}[/math] ).

 

[math]R_{gs}[/math] is a radius which cannot be compressed anymore due to the negative gravitational potential energy.

[beecee]

 

[math]R_{gs}[/math] is a radius which cannot be compressed anymore due to the negative gravitational potential energy.

GR disagrees with you, sorry.

And that has a pretty good track record.

But hey! If you believe you have found a genuine anomaly or error, then prepare a scientific paper for appropriate peer review.