Closed-form Absorption Probability of Certain D=5 and D=4 Black Holes and Leading-Order Cross-Section of Generic Extremal p-branes

TL;DR

This paper derives exact absorption probabilities for specific extremal black holes in D=4 and D=5, revealing frequency thresholds and connecting these to geodesic behavior, and also computes leading-order cross-sections for extremal p-branes.

Contribution

It provides the first closed-form solutions for absorption probabilities in certain extremal black holes and links these results to p-brane entropy and temperature relations.

Findings

Absorption probability vanishes below a frequency threshold.

Closed-form absorption probabilities are obtained for D=4 and D=5 extremal black holes.

Cross-sections match the entropy-temperature dependence in near-extremal p-branes.

Abstract

We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.