Singularity theorems in low regularity

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Written by Melanie Graf

Many classical results of general relativity require the spacetime metric to be at least twice continuously differentiable which is somewhat unsatisfactory from a physical point of view. In recent years there has been increased interest in low regularity spacetimes leading to proofs of both the Hawking and the Penrose singularity theorem for C^1,1-metrics (i.e., continuously differentiable metrics with Lipschitz continuous first derivatives). These proofs are based on new approximation techniques due to Chruściel and Grant which respect the causal structure. However, the more general singularity theorem of Hawking and Penrose has yet to be proven in this regularity.
       In my talk I would like to give a brief overview about the aforementioned proofs and discuss the various difficulties that arise when trying to prove the Hawking and Penrose singularity theorem in a similar fashion as well as our recent progress in overcoming (some of) those difficulties.