A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry

A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry Commun. Math. Phys. Communications in Digital Object Identifier (DOI) https://doi.org/10.1007/s00220-018-3157-1 Mathematical Physics A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry Jue Liu, Junbin Li Department of Mathematics, Sun Yat-sen University, Guangzhou, China. E-mail: liuj337@mail2.sysu.edu.cn; lijunbin@mail.sysu.edu.cn Received: 12 October 2017 / Accepted: 9 March 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract: Published in 1999, Christodoulou proved that the naked singularities of a self- gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role. 1. Introduction In the paper [4], Christodoulou proved both the weak cosmic censorship conjecture and the strong cosmic censorship http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-018-3157-1
Publisher site
See Article on Publisher Site

Abstract

Commun. Math. Phys. Communications in Digital Object Identifier (DOI) https://doi.org/10.1007/s00220-018-3157-1 Mathematical Physics A Robust Proof of the Instability of Naked Singularities of a Scalar Field in Spherical Symmetry Jue Liu, Junbin Li Department of Mathematics, Sun Yat-sen University, Guangzhou, China. E-mail: liuj337@mail2.sysu.edu.cn; lijunbin@mail.sysu.edu.cn Received: 12 October 2017 / Accepted: 9 March 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract: Published in 1999, Christodoulou proved that the naked singularities of a self- gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role. 1. Introduction In the paper [4], Christodoulou proved both the weak cosmic censorship conjecture and the strong cosmic censorship

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Jun 1, 2018

References

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