2015/07/02 by Jan Sbierski, Sbierski, Jan · 5 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.1507.00601
openalex publication_date 2015/07/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The maximal analytic Schwarzschild spacetime is manifestly inextendible as a\nLorentzian manifold with a twice continuously differentiable metric. In this\npaper, we prove the stronger statement that it is even inextendible as a\nLorentzian manifold with a continuous metric. To capture the obstruction to\ncontinuous extensions through the curvature singularity, we introduce the\nnotion of the spacelike diameter of a globally hyperbolic region of a\nLorentzian manifold with a merely continuous metric and give a sufficient\ncondition for the spacelike diameter to be finite. The investigation of\nlow-regularity inextendibility criteria is motivated by the strong cosmic\ncensorship conjecture.\n