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The Einstein-Klein-Gordon-AdS system for general boundary conditions

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Holzegel, G 
Warnick, CM 

Abstract

jats:p We construct unique local solutions for the spherically-symmetric Einstein–Klein–Gordon–anti-de Sitter (AdS) system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. This paper furnishes a starting point for such global investigations. </jats:p>

Description

Keywords

Anti-de Sitter, Klein-Gordon, initial-boundary value problem

Journal Title

Journal of Hyperbolic Differential Equations

Conference Name

Journal ISSN

0219-8916
1793-6993

Volume Title

12

Publisher

World Scientific Pub Co Pte Lt