Strong Cosmic Censorship with bounded curvature

Moritz Reintjes

doi:10.1088/1361-6382/ad636e

Strong Cosmic Censorship with bounded curvature

Moritz Reintjes

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

2 Citations (Scopus)

26 Downloads (CityUHK Scholars)

Abstract

In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in L^p. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W^1,p_loc, proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). © 2024 The Author(s).

Original language	English
Article number	175002
Journal	Classical and Quantum Gravity
Volume	41
Issue number	17
Online published	26 Jul 2024
DOIs	https://doi.org/10.1088/1361-6382/ad636e
Publication status	Published - 5 Sept 2024

Funding

M. Reintjes was partially supported by CityU Start-up Grant for New Faculty (7200748) and by CityU Strategic Research Grant (7005839).

Research Keywords

Strong Cosmic Censorship
optimal metric regularity
Lipschitz continuous metrics
uniform curvature bounds
elliptic partial differential equations

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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abstract = "In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W1,ploc, proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). {\textcopyright} 2024 The Author(s).",

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AU - Reintjes, Moritz

PY - 2024/9/5

Y1 - 2024/9/5

N2 - In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W1,ploc, proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). © 2024 The Author(s).

AB - In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W1,ploc, proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). © 2024 The Author(s).

KW - Strong Cosmic Censorship

KW - optimal metric regularity

KW - Lipschitz continuous metrics

KW - uniform curvature bounds

KW - elliptic partial differential equations

UR - https://www.scopus.com/pages/publications/85199685629

UR - https://www.scopus.com/pages/publications/85199685629#tab=impact

U2 - 10.1088/1361-6382/ad636e

DO - 10.1088/1361-6382/ad636e

M3 - RGC 21 - Publication in refereed journal

SN - 0264-9381

VL - 41

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 17

M1 - 175002

ER -

Strong Cosmic Censorship with bounded curvature

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