Singularities in general relativity

  • Jonathan Luk

    Department of Mathematics, Stanford University, 450 Jane Stanford Way, Stanford, CA 94305-2125, USA
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We survey some recent mathematical progress in understanding singularities arising in solutions to the Einstein equations. After some quick discussions of background material, we focus on the following three topics:

  • constructions of singular solutions to the Einstein vacuum equations,
  • the singularity structure in the interior of generic dynamical black holes and the relation to the strong cosmic censorship conjecture,
  • the formation of trapped surfaces, instabilities for the Einstein vacuum equations, and the relation to singularities.