Gravitational singularity

Question

Is it possible that the gravitational singularity actually turns out to be a genuine singularity once we have a true theory of quantum gravity in place? There is a lot of talk about singularity but the way it appears, most experts are attempting to 'purge' the singularity (Fuzz ball for instance) than actually considering the possibility that it can happen. Why hasn't it ever been considered that singularities don't always have to be mathematical artifacts, waiting to be swept under the rug?

Answer 1

Rather than asking quantum mechanics to get rid of a dressed singularity, it is possible to take an experimentally positivist approach and say that within the dress we should use a probability distribution for the position of the singularity, that goes to zero outside the dress surface (event horizon for a black hole type singularity). The simplest would be a uniform, static (not a function of time) distribution inside dress surface and 0 everywhere else, but others are possible, such as a delta function of position at one point inside surface at initial time, and a squared Schrodinger amplitude propagator at later times. From this probability for the position, follows a probability for different metric tensors that are solutions to vaccuum Einstein equation with the specified source singularity, over all spacetime, even outside the dress surface (or at least far enough away from any other sources, singular or not). One can impose physically meaningful constraints on the probability distribution, for example taking expectation values of metric tensor results in an average (no longer singular) energy momentum tensor, and integrating over all spacetime has to give correct answer for energy of the singularity (m c^2 in the case of a uncharged, non-rotating black hole), or other components of the resulting non-singular stress energy tensor. Treating singularities this way could be a path to deriving quantum mechanics from GR. One would need to study different kinds of spacetime singularities to see if any of them singles out the correct quantum mechanical probability distribution (squared propagator amplitudes) for elementary particle positions. Of course there is something missing here, which is the phase of the wavefunction, and how superposition of different position states leads to a convolution of the initial state with the propagator, but for amplitudes, not probabilities. I think Einstein was working on something similar to this proposal, where there is nothing but spacetime and matter results from singularities (radiation results from connection on the bundle of probability distributions). Perhaps I should post something separate to motivate this approach better.

Answer 2

The thing is that singularities being resolved is an entirely different thing. Fuzzballs are real, but in the full landscape of general relativity, singularities are just fine. I doubt resolution of singularities would be that singularities in general can be "removed". You are right that they don't have to be just mathematical things to be resolved. Most of the people working with these things don't see them that way -- for that matter, singularities are good! See https://physics.stackexchange.com/a/781724/365939, since I think I detailed a nice aspect of singularities. Singularities being physical has always been accepted; and for that matter resolving singularities in holographic quantum gravity has a no-go principle. I am not sure what the end product of the whole program would be, but I for one don't think they would be resolved.