Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

2022/11/28 by Christoph Kehle, Kehle, Christoph, Ryan Unger +1 · 16 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2211.15742

openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein-Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner-Nordström after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the "third law of black hole thermodynamics." The main step in the construction is a novel C^k characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner-Nordström event horizon with specified charge to mass ratio e/M. Our setup is inspired by the recent work of Aretakis-Czimek-Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk-Ulam theorem.

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