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.

arXiv comment15 pages, 4 figures. Invited review for the Theme issue "The future of mathematical cosmology" , submitted to Phil. Trans. A

References in corpus (23)

• Singularity Theorems and Their Consequences
• The 1965 Penrose singularity theorem
• Black hole singularities: a numerical approach
• Numerical Approaches to Spacetime Singularities
• Numerical simulations of generic singuarities
• Singularities in Inflationary Cosmology: A Review
• Singularities and Quantum Gravity
• Trapped surfaces and symmetries
• The Generalized Second Law implies a Quantum Singularity Theorem
• Quest for realistic non-singular black-hole geometries: Regular-center type
• Trapped surfaces
• Singularity theorems based on trapped submanifolds of arbitrary co-dimension
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• A singularity-free space-time
• Strongly Focused Gravitational Waves
• A singularity theorem based on spatial averages
• Ricci Fall-off in Static, Globally Hyperbolic, Non-singular Spacetimes
• A gravitational collapse singularity theorem consistent with black hole evaporation
• Black holes and closed trapped surfaces: a revision of a classic theorem
• The breakdown of weak null singularities inside black holes
• A new singularity theorem for black holes which allows chronology violation in the interior
• The boundary of the chronology violating set
• A New Type of Singularity Theorem

Cited by in corpus (10)

• The singularity theorems of General Relativity and their low regularity extensions
• The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics
• 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