Dear Salah

I am sorry. I apologize for my poor English.

======

In your comment,

We are trying to modify our theory to resolve the problem of singularity.

======

I insist that,

We can solve the problem of singularity by separating the term of gravitational self-energy(sum of the gravitational potential energy) from mass and including it in the solutions of field equation.

*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.

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, |U_gs| M' + ( - M_gs) or M + ( - M_gs)

Refer to chapter III-2-3.~III-2-6. P13~15

Data On Problems and Solutions of General Relativity - V2 (Commem...

Hi. I think that we never will know what happens inside of the black hole event horizon. By definition, this zone is forbidden for us. By other hand, though the existence of black holes is almost a scientific done, dont occurs the same with the existence of the singularities. These are just scientific conjectures.

In other words, we can consider to black holes are its own event horizons.

The language is misleading, unfortunately. What's meant is that spacetime, as probed by, non-inertial, observers can be described by a family of metrics, one member of that family can be identified as that of two black holes, another family can be identified as that of one black hole and it's possible to describe how to interpolate between the two metrics by a family that satisfies Einstein's equations. 

Your question is of course apposite in so far as in GTR black holes are of course singularities.

But there are other theories of gravitation that produce 2 polarizations without produicing singularities

The force of gravity in General relativity  (GR) is thought to come form the curvature of space-time.

Unfortunately the maths of GR implies infinite curvature and zero time passage at the black hole event horizon  and the black hole becomes a singularity- and yet the black hole has a radius.

The Misner Wheeler Thorne interpretation partially resolve this in  that the singularity rests inside the event horizon.

But yet another paradox arises if time stops at the event horizon (frozen star) no matter would fall in hence  black hole could not accumulate matter, and all the in-falling matter would be situated at or near the event horizon.

The solution is to alter the maths of GR.

Additionally GR falls down in a number of areas, so any new maths should also resolve these problems

Yes GR works in the weak fields of the the solar system, and Intermediate

fields of neutron stars. 

1). It produces infinite density singularities in the very strong fields

such as in black holes.

2).It does not necessarily explain dark matter in galaxy cores where we

know super-massive black holes exist and the galactic dark matter

therein,

3). It does not explain dark mater present in galactic halo's,and galactic

clusters such as the bullet cluster,

4).It does not explain the presence of cosmological dark matter as a whole.

5). It has not yet been fully corroborated by the studies of neutron stars

and in black holes.

6). It does not easily explain the presence of dark energy and cannot be

translated in quantum gravity.

Here I enclose a number of publications which explain all of these

phenomena, whilst agreeing with the results of GR where it has been

thoroughly tested.

1).First to obviate the infinite density singularities.

1a)

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity?ev=prf_pub

1b)

https://www.researchgate.net/publication/269689554_The_formulation_of_Dynamic_Newtonian_advanced_gravity_DNAg?ev=prf_pub

2).Secondly we explain the presence of dark matter at the centre of the

galaxy.

2a)

https://www.researchgate.net/publication/228858219_Advances_in_Black_Hole_Gravitational_Physics_and_Cold_Dark_Matter_Modelling._The_Gravity_of_Dark_Matter

3) Thirdly it is possible to explain the presence of dark matter in the

galactic halo.

3a)

https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo?ev=prf_pub

4). It is able to explain the presence of cosmological dark matter

https://www.researchgate.net/publication/32897680_An_advanced_dynamic_adaptation_of_Newtonian_equations_of_gravity

5). It is corroborated in neutron stars (including Data from radiation

damping ) and is corroborated by black hole studies.

5a)

https://www.researchgate.net/publication/32888463_An_advanced_modification_of_dynamicgravitation

5b).

https://www.researchgate.net/publication/269667939_Corroboration_of_Dynamic_Black_Hole_Gravitational_Physics_from_Observations_of_Cygnus_X-1

6) it explains dark energy and translates into quantum gravity

https://www.researchgate.net/publication/32899306_String_quintessence_and_the_formulation_of_advanced_quantum_gravity

Article An advanced dynamic adaptation of Newtonian equations of gravity

Article The formulation of dynamic Newtonian advanced gravity, DNAg

Article Advances in Black Hole Gravitational Physics and Cold Dark M...

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article An advanced modification of dynamic gravitation

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article String quintessence and the formulation of advanced quantum gravity

 If we we modify our theory to avoid the singularity, does a black hole without singularity still be a black hole? Or just become an accretion disc accumlate the matter around the center. See our ch.11: nonsingular black holes.

Book Advances in General Relativity Research

In that case it's necessary to explain how the singularity theorems are evaded. Just listing references isn't helpful; providing some insight is. The detection of gravitational waves by black hole merger isn't just a detection of those waves but, also, a check that the calculation of the strong gravitational fields generated in this case is, also, under control. In particular, since horizons are coordinate, not physical, singularities, they don't represent any problem of principle. 

The singularities of general relativity aren't any mathematical problem-any more than the singularities of functions in mathematics are-they're a physical problem. And they can only be resolved by a theory of short distance physics, that's consistent with general relativity at long distances.

Dear Stam: Black holes owe their existence to the presence of singularity. Singularity appears theoretically as a result to the Schwarzschild solution in asymptotically flat spacetime. Such an approximated Schwarzschild solution creates singularity (when r = 0). This false paradigm constitutes our observation. The observer is operating within a "paradigm". Observations being made are not complete in themselves, they interpreted within a theory (a paradigm). Schwarzschild solution singularity paradigm works as a lunette, through which we imagine that we could observe Black holes. Black holes have never been seen directly, their existence is just a matter of illusion. We did prove that the spacetime of the actual Universe is hyperbolic [S. A. Mabkhout, Phys. Essays 25, 112. 2012)]. Neither Schwarzschild metric nor Kerr metric possess singularity in the hyperbolic spacetime [S. A. Mabkhout, Phys. Essays 26, 422. 2013)] . So physically singularity does not exist, It just indicates a flaw in our mathematical model.

Dear Carlos Figueroa : The problem is that, according to Hawking there is no event horizon, instead there is an apparent horizon. Is the resultant black hole has an event horizon or an apparent horizon. Moreover what is the main character of the black hole? Is it the singularity or the event horizon (or apparent horizon) or both of them???  

It's useful to actually read Hawking and Penrose's paper:  http://rspa.royalsocietypublishing.org/content/314/1519/529

and then explain how the assumptions of the theorem are evaded, if it's claimed that this is the case. It pertains to the process of forming black holes-not, however, to the fact that black hole spacetimes themselves, as solutions of Einstein's equations can be checked to be valid, only to the limiting processes that lead to them.

The Schwarzschild (and Kerr) solution is an *exact* solution of Einstein's equations, not an approximate one. Once more it's wrong to confuse mathematics with physics. Whether astrophysical black holes exist or not can be debated, though to what purpose seems strange, now that measurements seem to confirm that their behavior can be accounted for, so they are a very good approximation-whether the mathematical expressions for the Schwarzschild or Kerr metric do solve Einstein's equations, with appropriate boundary conditions can be trivially checked to be true, so there's no point claiming otherwise. What the singularity theorem of Hawking and Penrose implies is that generic initial conditions lead to gravitational collapse-so if the claim is that such a collapse can be avoided, what should be spelled out is in what way the modifications evade the assumptions. 

The horizon is a coordinate, not a physical singularity-Kruskal showed how it can be avoided. An inertial observer reaches the singularity in finite proper time, a non-inertial observer doesn't see the singularity at all-can avoid it. 

Einstein's equations are, essentially, the only equations one can write down that possess general coordinate invariance, so any modification of them, that breaks that symmetry, in order that the usual exact solutions become ``approximate'', has consequences. 

The expressions for the metric in the linked article (a) don't satisfy Einstein's equations-since the spherically symmetric solution is unique-and (b) the statement, that they don't have a singularity because the radial velocity vanishes at r=0, isn't correct. What must be computed is the curvature scalar-but this is pointless, if the metric isn't a solution in the first place.

1- The Geometry describes the local structures of the manifold (spacetime). This can be done by local measurements and observation. It is not correct to generalize them to the global structures. The global structure of the spacetime can only be achieved by Topology. This can be done only with mathematics. We prove mathematically that the spacetime is globally hyperbolic [S. A. Mabkhout, Phys. Essays 25, 112 (2012)]. Although the perspective for nearby objects in hyperbolic space is very nearly identical to Euclidean space (i.e., the universe locally is approximately flat consistent with local observations.

2- The flat spacetime is an oversimplification to Einstein Field equations depend on assuming zero pressure and approximately zero local curvature. The laws of physics grows from flat spacetime paradigm do not fit the observed data at large structure. For this reason we brought mysterious ingredients such as inflation, dark matter and dark energy to adjust the laws of physics with observations and bridge the gap between theory and observations.

3- We have shown [S. A. Mabkhout, Phys. Essays 26,422 (2013)] that general relativity doesn't break down at large cosmological scale since it predicts both the accelerated expansion of the universe (without invoking dark energy) and predicts the galaxy flat rotation curve (without invoking dark matter).

4- The coefficients of the Schwarzschild metric basically are exponential functions (with infinite series of terms). When applied the initial condition due to the asymptotically flat spacetime, it reduces to an approximated factor (1-MG\r), by this mean it is an approximated.

5- The modified Schwarzschild metric is well derived mathematically [S. A. Mabkhout, Phys. Essays 26,422 (2013)].The modified Schwarzschild metric is not a different metric in a flat spacetime. It is the same metric based on a hyperbolic spacetime with different initial condition. Hence it is still a unique solution.

6- Hawking and Penrose singularity theorem pre-assumes a flat spacetime. If the spacetime is not flat, their singularity theorem does no longer valid.

7- The modified Schwarzschild metric in the hyperbolic spacetime  is not infected by singularity.. Hyperbolic spacetime prevent singularties to be formed or exist.

Article The hyperbolic geometry of the universe and the wedding of g...

Article The Big Bang hyperbolic universe neither needs inflation nor...

Dear Salah,

many thanks for Your excellent question that goes into the heart of the matter.Personally I have nothing against black holes and had published a host of papers on the Hawking effect. Yet my fear is connected with other facet of the model.One can apply any kind of fanciful toys he likes to construct a theoretical model. But the implication of the model for the explanation of really observed physical phenomenon  P-1 should not be ad hoc (Popper,Lakatos, Zahar). It means that the model should produce prediction of another phenomenon P-2 that can be observed independently of P-1.And I am afraid that this can not be done with the model of colliding black holes since the collision took place many many years ago.

The Schwaritschild radius for the sun is less than 3 km , hence for the two collided black holes are  3×32=96km and  3×29=87km. The space within a Galaxy is of order of millions of ligh years. How luckly those two black holes of such tiny sizes -at random- to have a chance to kiss each other ? In other wards what is the probabilty of this event to happen? Definitly, almost zero I guess.

The bottom line is that theory and computation predict that a binary black hole system will spiral together, radiating away momentum via gravitational waves with increasingly short wavelength (increasing frequency). With a final high frequency, high amplitude 'chirp', the holes can merge inside a highly distorted event horizon that quickly 'rings down' to a more settled state - again by radiating away energy in gravitational waves. It is precisely this set of signatures that an experiment like A-LIGO can look for.

Depending on the geometry of the collision and the spin of the holes, a fraction of the total mass of the original two holes will be lost as gravitational wave energy. So you might start with two holes totaling 100 solar masses, and end up with a hole of perhaps 95 solar masses. That may not sound so impressive, but we're talking about solar masses - a few 1030 kilograms of mass turning into gravitational radiation and being lost to the cosmos in a very short time. In other words, these black hole mergers can briefly be among the most luminous objects in the universe - except their luminosity is not in electromagnetic radiation, but in gravitational radiation.

There's one other little trick up the sleeve of a merging black hole system. If the black holes are asymmetric (with different masses for example) something very peculiar happens. As the holes merge they experience a recoil, and can shoot off across the cosmos. Another way of looking at this is to say that the center of mass of the system - the 'balance point' between the masses - follows a spiral path outwards as the holes spiral inwards. At the end, the whole system - the 'new' black hole - is moving, or recoiling off in some direction. 

https://www.youtube.com/watch?v=Tr1zDVbSjTM

https://www.youtube.com/watch?time_continue=2&v=p647WrQd684

Hi Rinat

I  did prove the spacetime is hyperbolic. The hyperbolic structure of the spacetime prevents the formation of singularity. Accrtion discs remain instead of singular plack holes. Such those tiny two objects (whatever they called black holes or else) have probability approches zero to merge compared to the Galaxy scale.

For me, the fundamental problem that we have with the black holes is that there isn't direct experimental confirmation of its existence. The evidence is indirect and we are swimming in a sea of conjectures. I am not specialist but there are two ideas about black holes that I seem wrong.

1)The singularity itself.

2) The separation of the space-time in two isolated regions separated by the event horizon.

I read the unpublished article of Hawking about this and, truly, this last conjecture seem have more sense.

For my part, I seem that the matter can be compacted beyond the Schwarzwild´s radius generating thus an object whose escape velocity is higher than c (or equal), but, on the other hand, the matter cant be compacted limitless.

Obiously, it is possible that the near of the event (or apparent) horizon, the conditions can be out of application range of our theories. (we always forget that our theories are limited).

Observatory (LIGO), the researchers detected ripples in the fabric of space-time called gravitational waves. But on that same day — less than half a second after LIGO made its monumental discovery — the Fermi Telescope, a space observatory orbiting the earth, picked up a brief, faint signal from the same region of space. The chances of that being coincidental hover around 0.2%. And if it wasn't a coincidence, it could open the door to a whole new world of physics. According to what we know about black holes, this shouldn't have happened: Light shouldn't be able to escape from two betrothed black holes since any gas surrounding them would be swallowed up by one before it merged. . But there's a problem with the gravitational-wave observatories we have now: They possess relatively blurry vision, according to NASA.

http://svs.gsfc.nasa.gov/cgi-bin/details.cgi?aid=12216

Chapter Nonsingular Black Holes

For decades, theory and observation suggested that stellar black holes couldn’t exceed roughly 10 solar masses.The black holes LIGO has seen, though, are somewhere in the middle—in the range of tens of solar masses. We’ve always assumed that black holes of this mass range should probably exist, but they’re hard to find evidence for in observations. So why has LIGO seen these, and not the smaller stellar-mass black holes everyone expected? But not everything is as physicists expected. The ripples we’ve seen were produced by black holes more massive than we thought we would find.

Where did such massive black holes come from?

How were such large black-hole binaries created? How did they form?”

One explanation is that: two pre-existing black holes came together by chance and captured each other gravitationally in some crowded part of the galaxy!

The Schwaritschild radius for the sun is less than 3 km , hence for the two collided black holes are  3×32=96km and  3×29=87km. The space within a Galaxy is of order of millions of light years. How luckly those two black holes of such tiny sizes -at random- to have a chance to meet each other ? In other wards what is the probability of this event to happen? Definitely, almost zero I guess.

A team of five researchers — James Creswell, Sebastian von Hausegger, Andrew D. Jackson, Hao Liu, and Pavel Naselsky — from the Niels Bohr Institute in Copenhagen, presented their own analysis of the openly available LIGO data. And, unlike the LIGO collaboration itself, they come to a disturbing conclusion: that these gravitational waves might not be signals at all, but rather patterns in the noise that have hoodwinked even the best scientists working on this puzzle.

Comments on our paper, 'On the time lags of the LIGO signals'

James Creswell, Sebastian von Hausegger, Andrew D. Jackson, Hao Liu, Pavel Naselsky

http://www.nbi.ku.dk/gravitational-waves/

Our recent arXiv posting of arXiv:1706.04191 "On the time lags of the LIGO signals" has generated considerable interest - both positive and negative. This is understandable given the significance of the claimed discovery of gravitational waves resulting from the merger of two black holes. In our opinion, a discovery of this importance merited a genuinely independent analysis of the data. It was the aim of our manuscript to perform such an analysis using publicly available data from LIGO and methods that were as close as possible to those adopted by the LIGO team. We focussed our attention mainly on the first event, GW150914, with special attention to the time lag between the arrival times of the signal at the Hanford and Livingston detectors. In our view, if we are to conclude reliably that this signal is due to a genuine astrophysical event, apart from chance-correlations, there should be no correlation between the "residual" time records from LIGO's two detectors in Hanford and Livingston. The residual records are defined as the difference between the cleaned records and the best GW template found by LIGO. Residual records should thus be dominated by noise, and they should show no correlations between Hanford and Livingston. Our investigation revealed that these residuals are, in fact, strongly correlated. Moreover, the time delay for these correlations coincides with the 6.9 ms time delay found for the putative GW signal itself.

Comments on our paper, 'On the time lags of the LIGO signals'

James Creswell, Sebastian von Hausegger, Andrew D. Jackson, Hao Liu, Pavel Naselsky

http://www.nbi.ku.dk/gravitational-waves/

As a member of the LIGO collaboration, Ian Harry states that he "tried to reproduce the results quoted in 'On the time lags of the LIGO signals'", but that he "[could] not reproduce the correlations claimed in section 3". Subsequent discussions with Ian Harry have revealed that this failure was due to several errors in his code. After necessary corrections were made, his script reproduces our results.

The fourth gravitational wave detection. The black holes that caused this latest round of gravitational waves were 31 and 25 times the mass of the sun before they merged, making this the second largest collision we’ve detected this way. They are located about 1.8 billion light years away from Earth. Again Ligo-Virgo detected a rare massive black holes merge for he forth time, while non of the expected existed black holes have been detected!!! What is wrong?

For a scientist, perplexity is the most exhilarating state of mind, because unexpected phenomena are often the most direct path to discoveries. And a recent observation from one of the furthest corners of the universe -- an ancient and enormous black hole -- has set the astronomical world buzzing. It is hard to understand how a black hole became so big, so long ago. So why is that surprising? Black holes are like humans. They start out small and they grow over time. This particular black hole existed when the universe was only about 5% of its current age, and was located so far away that the light signaling its existence is only now arriving on Earth, after traveling for about thirteen billion years.

http://edition.cnn.com/2017/12/10/opinions/quasars-black-hole-opinion-lincoln/index.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%253A+rss%252Fcnn_latest+(RSS%253A+CNN+-+Most+Recent)

Check the "Hawking radiation" in Wikipedia.

the singularity is unphysical. your answer can only be answered by a quantum gravity, which avoids singularities. .the singularity of a black hole is nothing but another word for the failure of geneal relativity at the planck scale. hence it makes no sense to ask for.the natue of the singularity