Is it possible that there are no singularities, even in black holes? Could there be another type of degeneracy pressure (after electrons and neutrons) that permits matter to compress enough to form an event horizon, but not a true singularity/ringularity? I know this is a poorly-understood area of physics but I'm curious if this particular possibility has been ruled out, and if it would have any relevance to BBT and cosmic inflation if it were found to be true.
Sure. A singularity is your theory crashing with a "not applicable in this regime" error. It means you need a better theory, in this case of how gravity behaves at high energy density. One possible take on it is fuzzballs:
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Is it possible that there are no singularities, even in black holes? Could there be another type of degeneracy pressure (after electrons and neutrons) that permits matter to compress enough to form an event horizon, but not a true singularity/ringularity? I know this is a poorly-understood area of physics but I'm curious if this particular possibility has been ruled out, and if it would have any relevance to BBT and cosmic inflation if it were found to be true.
Sure. A singularity is your theory crashing with a "not applicable in this regime" error. It means you need a better theory, in this case of how gravity behaves at high energy density. One possible take on it is fuzzballs:
https://en.wikipedia.org/wiki/Fuzzball_(string_theory)