  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.
