High Energy Reflection Coefficients of Black Holes and Branes

TL;DR

This paper analyzes how high-energy waves reflect off black holes and branes, revealing exponential suppression related to black hole singularities and temperatures, with implications for string theory and general relativity.

Contribution

It provides a new understanding of the exponential suppression of reflection coefficients at high energies and links this behavior to black hole singularities and temperatures, including in string theory contexts.

Findings

Reflection coefficient is exponentially suppressed at high energies.

Exponent fixed by black hole singularity and temperatures.

General bound on the exponent is half the inverse Hawking temperature.

Abstract

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.