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arXiv · 1610.06078

Boundary Causality vs Hyperbolicity for Spherical Black Holes in Gauss-Bonnet

Tomas Andrade·Elena Caceres·Cynthia Keeler
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Abstract

We explore the constraints boundary causality places on the allowable Gauss-Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss-Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss-Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss-Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

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Tomas Andrade, Elena Caceres, Cynthia Keeler. 2016-10-19. Boundary Causality vs Hyperbolicity for Spherical Black Holes in Gauss-Bonnet. https://doi.org/10.1088/1361-6382%2Faa7101

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