The Penrose singularity theorem in regularity $C^{1,1}$

Abstract

We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.

13 pages. Final version

References in corpus (4)

• Singularity Theorems and Their Consequences
• The 1965 Penrose singularity theorem
• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• Limit curve theorems in Lorentzian geometry

Cited by in corpus (27)

• Causality theory for closed cone structures with applications
• Spacetime Singularities and Cosmic Censorship Conjecture: A Review with Some Thoughts
• Global hyperbolicity for spacetimes with continuous metrics
• Singularity theorems for $C^1$-Lorentzian metrics
• The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
• Maximizers in Lipschitz spacetimes are either timelike or null
• The future is not always open
• On the causal hierarchy of Lorentzian length spaces
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• The singularity theorems of General Relativity and their low regularity extensions
• A Lorentzian analog for Hausdorff dimension and measure
• The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics
• Lorentz meets Lipschitz
• A Note on the Gannon-Lee Theorem
• Volume comparison for $C^{1,1}$ metrics
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• Twisted Black Hole Is Taub-NUT
• Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, II
• Synthetic versus distributional lower Ricci curvature bounds
• Hawking-type singularity theorems for worldvolume energy inequalities
• How Much NEC Breaking Can the Universe Endure?
• Green Operators in Low Regularity Spacetimes and Quantum Field Theory
• A nonlinear theory of distributional geometry
• Non-smooth gravity and parity violation
• A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity
• A Scale-Dependent Distance Functional between Past Light Cones in Cosmology