The Klein-Gordon equation on the toric AdS-Schwarzschild black hole
Classical and Quantum Gravity
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Dunn, J., & Warnick, C. (2016). The Klein-Gordon equation on the toric AdS-Schwarzschild black hole. Classical and Quantum Gravity, 33 (12)https://doi.org/10.1088/0264-9381/33/12/125010
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.
External DOI: https://doi.org/10.1088/0264-9381/33/12/125010
This record's URL: https://www.repository.cam.ac.uk/handle/1810/282792