  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 $(D-2)$-dimensional maximal symmetry, including
spherically symmetric and flat spaces. If the geometrical null energy
condition, $R_{AB}N^AN^B \ge 0$ 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.
