High Energy Reflection Coefficients of Black Holes and Branes

We study the reflection coefficient associated with a wave that scatters off various black holes in general relativity. We show that for large energies, compared to the scale set by the curvature, the reflection coefficient is suppressed exponentially with the energy. We find that the exponent is fixed by the singularity of the black hole to be $\frac12(\beta+\beta_{in})$ where $\beta$ is the inverse Hawking temperature and $\beta_{in}$ is the inverse temperature associated with the inner horizon. We also study the reflection coefficient associated with extremal D3-branes in string theory. In that case, the exponent is determined by a fictitious singularity located in the complexified space-time. Generalizations to M2-branes and M5-branes are also discussed. We argue that $\frac12 \beta$ is a general bound on the exponent.