The Klein-Gordon equation on the toric AdS-Schwarzschild black hole
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Dunn, J
Warnick, Claude https://orcid.org/0000-0001-7132-8319
Abstract
We consider the Klein-Gordon equation on the exterior of the toric anti de-Sitter Schwarzschild black hole with Dirichlet, Neumann and Robin boundary con- ditions at I. We define a non-degenerate energy for the equation which controls the renormalised H1 norm of the field. We then establish both decay and integrated de- cay of this energy through vector field methods. Finally we demonstrate the necessity of ‘losing a derivative’ in the integrated energy estimate through the construction of a Gaussian beam staying in the exterior of the event horizon for arbitrary long co- ordinate time.
Description
Keywords
anti de-Sitter spacetime, black hole, Klein-Gordon equation
Journal Title
Classical and Quantum Gravity
Conference Name
Journal ISSN
0264-9381
1361-6382
1361-6382
Volume Title
33
Publisher
IOP Publishing