Mass distribution inside the event horizon

[PaulMurphy]

In the popular physics books that I enjoy reading, black holes are described as containing a singularity of zero volume that contains 100% of the mass. I can't envision this, since 100% of the spacetime inside the event horizon would then be empty space except for virtual particles.

Is this description of infinite density a result of the math, with the possibility of there being a minimum volume in actuality? I have the impression that our Universe has quantized out a lot of potential infinities, such as electron orbits, Planck limits and possible pixelated spacetime. I assume that in order for a Universe to be calculated by a computer or experienced by a brain, the infinities have to be pared down to finitely calculable values.

 

[PaulMurphy]

I searched related threads and I found a reply to my question that made a lot of sense to me. I'll post it below.

Actually, very few physicists believe in singularities. Typically, infinities indicate the failure of a model in some domain -- for example, the ultraviolet catastrophe was an infinity that resulting in the development of quantum mechanics. When infinities appear, it's usually a sign that something is in need of quantization. In the case of black holes, it is gravitation that needs to be quantized. The competing theories for this quantization are string theory and loop quantum gravity. Both promise to remove the singularity from the model.

- Warren

 

[qraal]

I searched related threads and I found a reply to my question that made a lot of sense to me. I'll post it below.

It's a fair assessment of the situation, but currently there's no front runner in the field of possible solutions to the singularity problems in GR or QM for that matter.

However it's a mistake to think the infinities can't exist because we can't compute them. Transfinites have a long and venerable history in mathematics, even if we have trouble wrapping our brains around them.

On a related point, inside a spinning black hole the singularity isn't a point, but a ring. Still infinitesimal volume, but it does have a finite size.

 

[Orion1]

According to Loop Quantum Gravity, all wave packets incident upon a infinitesimal singularity 'bounce off'. The result is a Equation of State that oscillates between kinetic energy and gravitational potential energy of the order of a quantized Planck volume. Therefore, infinite dimensions on infinitesimal scales do not exist in the Universe, all dimensions become quantized instead.

This theory is also used in 'Big Bounce' theory in Astrophysics and Cosmology.

Note that General Relativity does not describe physical laws below a Planck singularity. Absent Quantum Gravitation, nobody can claim with absolute certainty that infinite dimensions on infinitesimal scales can actually exist in the Universe.

The closest simple conventional analogy I can think of is the spatial distance between a photon and a mirror. When the spatial distance between a photon and a mirror becomes zero (a singularity), the photon reflects off the mirror. A mirror and a zero spatial dimension (a singularity) can both be described classically as impenetrable barriers of infinite height.
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