What Happens to Gravity and Temperature at the Center of a Black Hole?

[qraal]

graal is not referring to the "central" crushing singularity, graal is referring to the weak singularity at the inner (Cauchy) horizon of roating and electrically charged black holes. Seminal work on this was done by Poisson and Israel, and this work was continued by Ori. See

http://physics.technion.ac.il/~school/Amos_Ori.pdf ,

particularly pages 15, starting at "Consequence to the curvature singularity at the IH: (IH = Inner Horizon), 16, and 24.

For Novikov's take on this, see

http://arxiv.org/abs/gr-qc/0304052.

Roughly, if components of g (the metric) are continuous but "pointy" (like the absolute value function), then first derivatives of g have step diiscontinuities (like the Heaviside step function), and second derivatives of g (used in the curvature tensor) are like Dirac delta functions. If a curvature singularity blows up like a Dirac delta function, then integration produces only a finite contribution to the tidal deformation of an object, which, if the object is robust enough, it can withstand.

Thanks George. That's what I meant. Though he has interesting things to say about non-spinning BHs too.

 

[Chronos]

Wallace is correct. Game over when you reach the event horizon of a black hole.

 

[MeJennifer]

The really important point is, again as other have stated, that this is the property of the black hole solution in GR and this theory is almost certainly inadequate, and a better theory would not go singular. It is really important to stress that a singularity is not a physics thing it is just a mathematical property of a particular solution to general relativity, which probably suggests that the theory is incomplete.

Well, to rock the boat just a little bit, is that definably true?

For instance many solutions that have a singularity have an asymptotic flatness assumption. If a spacetime is almost flat far away from the possible black hole or even negligibly curved then the singularity may never form. And then there is the assumption of a point mass. To my thinking general relativity might imply a non-local notion of energy-momentum, so yes if we force the thing to be a point then perhaps we should not be surprised we get a singularity.

 

[Wallace]

We don't 'force' the centre of a black hole to be a point, physics does. Once the Schwarzschild radius of a body is greater than the radius of that body then all null future null paths of all points within the body end up at r=0, hence collapse to a 'singularity' is inevitable, given GR. We can also, noting other known physics, work out the stages of collapse of a dense object before it gets to this run-away collapse. For instance at certain critical densities various forces are overcome, turning the star into different states (e.g. white dwarf -> Neutron star -> Quark star...). Given the physics we know, stars of certain masses will inevitably collapse to blacks holes, so we don't need to construct the BH solution from scratch, we can actually see that real objects will evolve to that state given reasonable initial conditions.

The only way out is unknown physics, which is possible given the present problems with the theories.

Asymptotic flatness is merely a requirement enforced if you are looking at a vacuum solution. There is no reason that in a non-vaccum solution BH's can't form (i.e. a collapsing sphere in an FRW background) it just makes the maths a little more complicated, so textbook derivations often simplify things to a vacuum solution. The process of singularity formation has nothing to do with the conditions at infinity though, as you would expect since GR is a purely local theory.