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

TL;DR

This paper investigates how boundary causality and hyperbolicity constraints limit Gauss-Bonnet gravity couplings in asymptotically AdS spherical black holes, revealing that hyperbolicity considerations are crucial for understanding causality bounds.

Contribution

It demonstrates that hyperbolicity constraints are essential in determining the causality bounds for Gauss-Bonnet couplings in spherical black holes, aligning these bounds with planar cases.

Findings

Spherical black holes violate boundary causality at smaller couplings than planar ones.

Hyperbolicity violations occur before causality violations for negative couplings.

Causality bounds from spherical black holes are comparable to those from planar black holes.

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.