A critical appraisal of the singularity theorems

Abstract

The 2020 Nobel prize in Physics has revived the interest in the singularity theorems and, in particular, in the Penrose theorem published in 1965. In this short paper I briefly review the main ideas behind the theorems and then proceed to an evaluation of their hypotheses and implications. I will try to dispel some common misconceptions about the theorems and their conclusions, as well as to convey some of their rarely mentioned consequences. In particular, a discussion of spacetime extensions in relation to the theorems is provided. The nature of the singularity inside black holes is also analyzed.

15 pages, 4 figures. Invited review for the Theme issue "The future of mathematical cosmology" , submitted to Phil. Trans. A

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• Compact objects with scalar charge embedded in a magnetic or electric field in Einstein-Maxwell-dilaton theories
• Spacetime singularities and curvature blow-ups
• How Much NEC Breaking Can the Universe Endure?
• Hawking-type singularity theorems for worldvolume energy inequalities
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• Singularity and differentiability at the origin of static and spherically symmetric black holes
• Penrose's singularity theorem and the Kerr space-time
• Nonsingular spherically symmetric black-hole model with holonomy corrections