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The Hawking–Penrose singularity theorem for C1,1-Lorentzian

Graf, M, Grant, James, Kunzinger, M and Steinbauer, R (2017) The Hawking–Penrose singularity theorem for C1,1-Lorentzian Communications in Mathematical Physics, 360 (3). pp. 1009-1042.

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Abstract

We show that the Hawking–Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C1 , 1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C1 , 1-metrics, and of C0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Graf, M
Grant, Jamesj.grant@surrey.ac.uk
Kunzinger, M
Steinbauer, R
Date : 30 November 2017
DOI : 10.1007/s00220-017-3047-y
Copyright Disclaimer : The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s00220-017-3047-y
Uncontrolled Keywords : Singularity theorems, low regularity, regularisation, causality theory
Depositing User : Melanie Hughes
Date Deposited : 24 Oct 2017 10:15
Last Modified : 30 Nov 2018 02:08
URI: http://epubs.surrey.ac.uk/id/eprint/842633

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