What if singularities are massless? [closed]

Question

I've read that singularities theoretically have an infinite density (probably due to zero volume), but what if there is no mass in it? It could be that any object that enters a black hole probably undergoes infinite amount of acceleration and gets converted into energy and since energy doesn't require volume, it could confine in a place with zero volume.

The exact question: Is it possible that singularities don't have mass but only energy? Justify.

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Answer 1

I know that it is common parlance in popular physics literature to talk about "pure energy," but this isn't a particularly useful term -- in modern physical theories, the underlying concept is that everything in the universe is made up by fields. All fields have some form of energy associated with them, and the energy of a closed system is equal to the mass of that closed system.

In more direct terms, energy is a property of matter, or at least of a field. If some infinitesimal region of a field has a finite energy, you don't get away from any of the singularity problems.

Answer 2

The singularity of a black hole is a region where the classical physics of general relativity fail. The curvature diverges and the differential equations make no predictions. We can as a rule of thumb consider a cut off at the Planck scale. The acceleration can be computed with the geodesic deviation equation $$ \frac{d^2x^a}{ds^2}~=~{R^a}_{bcd}V^bx^cV^d $$ which measures the rate two test masses separate with $|V^b|~\simeq~c$. The curvature is at the maximum Planck unit $R~\sim~\ell_p^{-2}$ $=~3.8\times 10^{65}cm^{-2}$. Near the singularity we look at a Planck unit distance $|x^c|~\simeq~\ell_p$. The computed acceleration is then $a~\simeq~1.5\times 10^{49}m/s^2$. This is the maximum acceleration possible, at least based on this calculation.

Using energy and force we might also make an estimate. We have force $F~=~\frac{\delta E}{\delta x}$ and let us assume the energy is a Planck unit. We assume a quantum system approaching the singularity will be excited by energy up to the Planck energy. So this force is Planck energy divided by the Planck length, or $F~=~1.96\times 10^9j/1.62\times 10^{-33}cm$ $=~1.2\times 10^{42}N$. Now if we divide by the Planck mass $M_p~=~2.18\times 10^{-8}kg$ we get $a~=~5.6\times 10^{49}m/s^2$. This is a little bigger than the geodesic equation estimation, but we all have the idea that there is a Planck acceleration that is really large.

In the Schwarzschild metric the singularity is a spatial surface, which in a sense is the future spatial surface of any object that enters the black hole. At this point general relativity breaks down. Vafa has shown this may be a condensate of tachyons. Since black holes exchange entanglement across the horizon in the ER=EPR setting, maybe these are a form of nonlocal hidden variable. If so then these are really not that physical, but form a sort of gadget or device for quantum gravity calculations.

What occurs on a black hole singularity may not have a description according to understood physics. Saying that matter becomes energy does not help much, for that energy is in a sense compresssed into a tiny region.