Today I was invited to give a tiny talk about my current research in my master’s thesis. In 15 minutes I had the opportunity to explain to the audience the concepts a black holes, naked singularities and to tell them something about my ultimate goal of quantizing solutions of Einstein’s field equations that have naked singularities as solutions.
In the first part I talked a little bit about the so-called Schwarzschild solution. There I have shown in a hand-waving way that there are two types of singularities. The first type is a real singularity and the other type was a so-called event horizon which is a surface in spacetime that has the property, that if you pass it, you are doomed to fall into the black hole and there is no way to escape this fate. Summarized, there is no way to escape from a singularity since there is an event horizon surrounding it, i.e. no communication to the outside is possible.
A naked singularity is now the case where a real singularity is not hidden behind an event horizon. In several calculations people have shown that this are ‘real’ solutions for some choices of initial data. In particular in the case of the so-called LTB-model it is possible to write down analytical solutions that have a naked singularity in the center. This is the sage of my current work.
Also I have shown that the existence of naked singularities violates the notion of causality, i.e. there are closed curves in spacetime itself. For example I could travel through a naked singularity back in time to kill my father. In order to avoid these weird phenomena Roger Penrosé imposed in 1969 the so-called cosmic censorship hypotheses, which tells that under certain initial conditions a formation of a naked singularity is not possible. But since naked singularities predict somehow predict the breakdown of general relativity itself one tries to solve this:
One idea is, that naked singularities or singularities at all are only one artifact of general relativity which result from the fact of neglecting quantum mechanical effects. Therefor in the last part of my master thesis I will try to ally to procedure of canonical quantization to a solution of Einstein’s field equations that admit a naked singularity. If everything works properly I will study the properties of my solution. I am really looking forward to this because the result is completely unknown and even wage predictions are not possible at all.
You can find the slides to my talk here.