Causal structures in Gauss-Bonnet gravity

Abstract

We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the ``event horizon'' in the sense of causality. We also analyze causal structures on nonstationary solutions with $(D\ensuremath{-}2)$-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, ${R}_{AB}{N}^{A}{N}^{B}\ensuremath{\ge}0$ for any null vector ${N}^{A}$, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the ``black hole'' defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.