Does mass dissipate in a black hole?

[Bengey]

Thinking about how so much matter can be squeezed into a singularity, the answer (if I understand correctly) is that the matter just stacks upon itself down an infinitely long weird space-time well. In a sense, the last item in masks the ones below.
But doesn't this impact the gravitational heft of the black hole ?
The matter at the bottom of the well, it seems, should behave gravitationally as if it is farther away from the surface that we experience. If so, the black hole should "weigh" less than the sum of what went into it, so in effect matter would appear to be lost, gravitationally speaking.
And if that's the case (long shot), does it impact the calculations of dark energy ? The assumption has been that matter is not destroyed, but what if it is being "masked" by the black hole, so that over time as more matter falls into black holes there is less gravitational energy restricting the expansion of the universe ?

 

[pervect]

Thinking about how so much matter can be squeezed into a singularity, the answer (if I understand correctly) is that the matter just stacks upon itself down an infinitely long weird space-time well. In a sense, the last item in masks the ones below.
But doesn't this impact the gravitational heft of the black hole ?
The matter at the bottom of the well, it seems, should behave gravitationally as if it is farther away from the surface that we experience. If so, the black hole should "weigh" less than the sum of what went into it, so in effect matter would appear to be lost, gravitationally speaking.
And if that's the case (long shot), does it impact the calculations of dark energy ? The assumption has been that matter is not destroyed, but what if it is being "masked" by the black hole, so that over time as more matter falls into black holes there is less gravitational energy restricting the expansion of the universe ?

The short answer is no, not really.

The longer answer is that GR doesn't have a single definition of mass, there are al least 4 that can be applied to a black hole or other gravitating system. However, none of the big 4 (the Komar mass, the ADM mass, the Bondi mass, or the parameter M in the Schwarzschild metric) do not vanish for a black hole. In fact they are all equal.

If you measure orbital parameters of a distant object orbiting the black holes and apply Newton's laws, defining the "radius" by the circumference divided by 2 pi (which is equal to the Schwarzschild R coordinate), you'll find that the mass of the black hole computed via this method matches the Schwarzschild mass parameter M (from the metric), which matches the other three.

 

[PeterDonis]

Thinking about how so much matter can be squeezed into a singularity, the answer (if I understand correctly) is that the matter just stacks upon itself down an infinitely long weird space-time well.

Not really. According to classical GR, the matter disappears when it reaches the singularity, so thinking of it as being "squeezed into the singularity" is not correct. (Note that the "mass" of the black hole, as measured from the outside, is still there even though the matter disappears when it reaches the singularity; that's because the mass of the hole is really due to the spacetime curvature around the hole, not the matter inside it, and that spacetime curvature, once formed by the collapsing matter, can maintain itself without any matter present.)

However, according to classical GR, spacetime curvature becomes infinite at the singularity, and the standard view is that this shows that classical GR is incorrect in this regime. On this view, we won't really have a consistent view of what happens close to the singularity until we have a theory of quantum gravity. There are various speculations about what might happen in this regime, but nothing definite is known.

 

[Bengey]

Four definitions of mass ? Things have changed since I took physics classes !
Can space-time curvature really maintain itself without anything inside ? Or is it just the distinction between matter and mass, so you mean the mass is still necessary to maintain the curvature ?
How did the standard graphic of a well in a rubber sheet lead me astray into thinking that there is mass at the bottom, some large "distance" away from the undisturbed "surface" ? Is that image not valid in this respect ?
Do the GR equations not consider that mass inside the singularity might lose its "oomph" because it is more "distant" ? Hey, maybe that's a fifth kind of mass ! Sorry for the quotation marks, and when I get a chance I'll read up on those mass definitions.

 

[PeterDonis]

Can space-time curvature really maintain itself without anything inside ?

Yes. A black hole (at least in the idealized case we're talking about here) is a vacuum solution: there is no stress-energy anywhere. So any spacetime curvature present must be able to maintain itself in the absence of any source.

Is that image not valid in this respect ?

Yes. In fact, that image is misleading in a number of respects, and I don't recommend using it to try to understand a black hole.

Do the GR equations not consider that mass inside the singularity might lose its "oomph" because it is more "distant" ?

No; that's not what happens to the collapsing matter that forms the hole when it reaches the singularity. It just disappears according to classical GR.

As I noted before, we believe that classical GR is not correct in this regime, but none of the proposals for quantum corrections in this regime involve matter falling through the singularity (or where the singularity would have been in the classical model) and having diminishing effect on the spacetime outside the hole's horizon because it is getting "further away". So even with quantum corrections, as far as we can tell, the answer to your question is still "no".

 

[phinds]

How did the standard graphic of a well in a rubber sheet lead me astray... ?

Because you seem to be trying to apply it INSIDE the EH of a BH and that is NOT what that analogy is even remotely good for. It is a seriously flawed analogy but to the extent that it is meaningful at all it only applies outside the EH's.

 

[Vanadium 50]

The OP's question has been answered, but since then the thread has diverged into some highly speculative grounds.