We really know very less about the black hole. The mathematics that we are knowing might not be able to explain the black hole clearly. More and more research works will give some very convincing idea about it. 

I aqgree, although this is not my field I understand that knowledge on black holes is very limited and which is worse, not completely proved.

"What really happens inside a black hole?"

This question apparently depends on how you define the black hole. When taking the Schwarzschild radius Rs ~ GM/c2 as the event horizon of included mass M, this apparently fits quite reasonably with the extent of our visible Universe. So what happens inside, in particular, is what you are just experiencing in your here and now.

I offer a naive interpretation as a foil for thought. According to quantum field theory [aka Quantum Electrodynamics (QED)] the "vacuum" of empty space is a seething froth of particles and their antiparticles thanks to Einstein's E = mc2 and Heisenberg's uncertainty principle ∆t ~ h/∆E. These particles continually come and go in virtually infinitesimal moments of time. Black holes have mass (and energy by Einstein's dictum), angular momentum, and little else obsrvable from the exterior. My understanding of the Schwarzschild solution suggests that at the event horizon (at the Schwarzschild radius RS)the radial coordinate r and the time t effectively reverse roles so that the singularity becomes t → 0 and r remains finite so the black hole has finite volume. So with the finite energy E of the black hole, the uncertainty principle, and Einstein's dictum we could have a homogeneous isotropic sea of all of the particles of the universe! Cute but I suppose unlikely.

@Johan

I agree with your premise but few in the mainstream do.

Here is an interesting video

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

Andrew:

Thanks for the link, I've seen it and the following video as well. My conclusion: Plenty of phantasy, but by far not sufficient for reliably deducing "reality". Mainstream communities often are stuck to and enjoy funding on the basis of popular (spectacular) premises like Big Bang, Black Holes, Dark Matter, and the like to the disadvantage of less spectacular while sometimes quite valuable alternative approaches. Our current refereeing and funding system expectably offers the best warranty for long term mainstream support. ResearchGate and other open discussion boards, I hope, will help us escape the trap.

Andrew you have correctly interpreted Albert Einstein's field equations. In fact the field equations as they stand are exactly what you described. I make the exception for QM that the mathematical singularity has physically representation of exactly one Planck volume, explaining the appearance of an event horizon as the relativistic transformation of surface size integrated over a gravity field.

Black hole structure was largely fixed in science until about 1964 when cosmic microwaves were discovered. Radiation makes a problem for black holes that Stephen Hawking and Roger Penrose attempted to fix in their NATURE OF SPACE AND TIME, almost 30 years later. They proposed that collapsed stars are never completely black because of QM effects near the event  horizons. They developed a model of thermodynamic equilibrium, heat balance and very low temperature of a black hole.  I subscribe to their methods but use gravity potentials to calculate the blue shifted temperature of microwaves, resulting in a very high temperature approaching Planck temperature. Already Hawking and Penrose have deviated from Einstein field equations just enough to introduce a physical reality into the mathematical abstraction. I go a bit further, but mostly in private correspondence.

The 2,7 degree Kelvin microwave of cold space gets blue shifted to Planck temperature as it approaches an event horizon, or red shifted from Planck temperature to 2,7 degrees Kelvin as it departs from a collapsed star. The collapsed star is very dark gray observed from a great distance, but appears white hot when approaching an event horizon.

Again from Hawking and Penrose, the event horizon size is only referenced to an observer at infinite distance. Closer observers measure a smaller size, continuing to appear smaller yet until the ashes of the most determined traveler vaporize at some small distance from the Planck sized singularity. A distant observer of course doesn't see any of this because of time transformations, except the traveler appearing to stop short of the event horizon and stay there for ever.

For the traveler it's like a one way trip to Hell, quickly destroyed, but appearing to the not so distant observers as an eternity of torment in flames. This part was not from Hawking and Penrose. Most of science has not even understood Einstein yet.

In conclusion you have correctly interpreted Einstein, but now need to reed Hawking and Penrose NATURE OF SPACE AND TIME, looking for the black hole modifications. When finished with that you might consider my higher temperature version.

AW: We are all told that a black hole is a singularity where time stops and inside the black hole there is no space and the black hole itself has no volume. Does anyone really believe that is the case or is there something wrong with the maths here.

The maths has limitations but before that there is something wrong with your sources, none of those points are the mainstream view.

@George

Perhaps then you need  to edit Wikipeadia to set them straight- see just how far you get.

"At the center of a black hole, as described by general relativity, lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[61] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity that lies in the plane of rotation.[62] In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[63] The singular region can thus be thought of as having infinite density."

Wikipedia: At the center of a black hole ... lies a gravitational singularity

That is roughly correct*.

AW: .. a black hole is a singularity ..

That is not.

Wikipedia: The singular region has zero volume

That is correct.

AW: .. the black hole itself has no volume ..

That is not.

* Strictly, the word "singularity" should be taken to indicate where the maths reaches its limitation rather than a physical object, and "center" should be considered in a time-like sense.

Sigh. A Kerr-Newman black hole has a fairly complicated internal structure, and so do other forms of black holes. GD is right. The original question is badly mistaken in its premises.

A simple Google search on "black holes" will give the searcher modern information on the internal structures of black holes - in words and in pictures.

On the other hand, most of our knowledge of black holes is purely theoretical and we are just beginning to get some actual observational evidence to work with (see LIGO discoveries). While the theoretical models may correctly identify the basic properties of black holes, there are undoubtedly many details of their inner structure that remain unknown at present.

RLO

http://www3.amherst.edu/~rloldershaw

Fractal Cosmology/ Discrete Scale Relativity

Andrew the original field equations of Einstein rather simply say that the volume inside a closed surface is less than the surface size and shape would predict. That's what the Ricci tensor does. The stress energy term tells how much smaller the volume is in curved space than it would be in flat space. The other term called a trace was added last and as an after thought  to make the volume calculate correctly with no stress energy, like a boundary condition in the math.

That said and as GD pointed out your statement does not represent the prevailing view in science. At one time it did represent the views of the very few people who understood the field equations. Black hole theories have been developed to the point they do not agree with Einstein's field equations exactly, but close enough that a quantum deviation can explain the differences. The field equations are good enough for most purpose, and the black hole models are good enough for other purposes.

Einstein pointed out in his last writing at the end of Appendix V in his non technical book 15th edition of 1952 that the field theories are not complete and he would like his readers to continue developing them. 

People who understood the field equations never claimed that the Schwarschild radius of a generic black hole was zero!  Right?

Robert "People who understood the field equations never claimed that the Schwarschild radius of a generic black hole was zero!  Right?"

You are correct. The Schwarschild radius has always been the same [ r = 2MG/c2 ] and also agrees with Newtonian calculations. [ (1/2)v2 =  MG/r ] for velocity approaching light speed. The point I made about it in reference to Hawking and Penrose is that the  Schwarschild radius is measured by an observer at infinite distance from the black hole.

Penrose wrote in Chapter 2, THE NATURE OF SPACE AND TIME, Princeton University Press, Oxford, 2000, page 29 in the paper back edition first printing. "there is some region that cannot send signals to infinity. The boundary of this region is the event horizon."  This is the point I hope readers will understand. The Schwarschild radius is not completely black to observers at finite distance.

For observers at radius r0 less than infinity the apparent event horizon for the non rotating black hole has radius r.

r = (2MG/c2)/{ 1+ (2MG/r0c2) }

When a traveler approaches the Schwarschild radius the apparent radius of the event horizon has decreased to half of the Schwarschild radius. The Schwarschild radius never gets smaller for the same mass. The apparent event horizon for a traveler does. This is why Hawking was able to do his QM and TD revisions of black hole theory to accommodate cosmic background microwaves entering a black hole and coming out again as quantum events. Hawking's thermodynamic equilibrium is exactly as much radiation energy coming out as is going in, but not coming out to infinity, just coming out into a large but finite region . Then his calculated temperature of the black hole increases until the equilibrium is established.

For the traveler I don't believe the radius ever goes to zero. More likely something bad happens to end the journey. A lot of people have different opinions about black holes. If they get the blue shifted microwave temperature correct, then a lot of those other opinions may change.

JD: For the traveler I don't believe the radius ever goes to zero.

That is correct, the horizon moves ahead but also wraps round behind him to become a bubble. There's a very good site by Andrew Hamilton explaining the conventional view linked.

http://casa.colorado.edu/~ajsh/schw.shtml