A gravitational collapse singularity theorem consistent with black hole evaporation


The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work, I show that the causality conditions in Penrose’s theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence compatibly with quantum field theory and black hole evaporation.

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    Introduced a complete Riemannian metric h, this result follows from the application of the limit curve theorem to a sequence of h-arc length parametrized causal curves of the form \(\sigma _k(t)=\sigma (t-a_k)\) where \(a_k\) is a diverging sequence. Since the h-arc length of the curves on both sides of the new origins \(\sigma (-a_k)\) diverges, the limit curve that passes through an accumulation point of \(\{\sigma (-a_k)\}\) is inextendible rather than just past inextendible; see the references for details.


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Useful conversations with Ivan P. Costa e Silva, José Luis Flores, Miguel Sánchez and José Senovilla, and useful comments by the referees are acknowledged. Work partially supported by GNFM-INDAM.

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Minguzzi, E. A gravitational collapse singularity theorem consistent with black hole evaporation. Lett Math Phys (2020). https://doi.org/10.1007/s11005-020-01295-9

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  • Singularity theorems
  • Black holes
  • Causality

Mathematics Subject Classification

  • 83C57
  • 83C75
  • 53C50