Abstract
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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Notes
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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Acknowledgements
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 110, 2383–2396 (2020). https://doi.org/10.1007/s11005-020-01295-9
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DOI: https://doi.org/10.1007/s11005-020-01295-9