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I was watching this PBS spacetime video which made the case that mass is just a form of bound energy. Essentially massless particles are confined in a small space giving particles the illusion of mass.

Since the heat and pressure inside a black hole is essentially infinite, does that mean that matter can't hold its form at the singularity and therefore reverts back into energy via $E=mc^2$?

Wouldn't the converse (elementary particles keep their mass) lead to infinities (which are impossible) as the black hole tries to infinitely compress particles at the singularity? Should the singularity be instead described as a peak in the energy field of the Universe, instead of a physical object?

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I would suspect that the temperature near the singularity would exceed the maximum temperature for spontaneous symmetry breaking to take place. Therefore, all elementary particles would be massless.

Bones
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When something enters the BH event horizon, the most important thing to understand is that the theoretical escape velocity becomes more then c.

Now, this will cause gravity to overcome all the other forces' strength even on the QM scale (because all forces propagate at speed c), thus crushing/tearing all types of matter apart, even overcoming:

  1. EM forces, that hold the electrons around the nucleus, thus atoms seize to exist

  2. residual strong forces (nuclear forces), holding nuclei together, thus nuclei seize to exist

  3. strong forces, that hold the nucleons' quarks together, thus protons and neutrons seize to exist,

  4. quarks become unconfined, and gluons too, flying around at speed c freely like photons, since both are massless. So yes, everything essentially becomes energy inside the BH horizon (though leptons are still massive).

Please see here:

https://physics.stackexchange.com/a/45001/132371