Low-frequency scalar absorption cross sections for stationary black holes

TL;DR

This paper establishes that the low-frequency scalar absorption cross section for stationary black holes equals the horizon area under certain conditions, extending previous results to rotating and non-spherical black holes.

Contribution

It proves the equality of the zero-frequency absorption cross section and the horizon area for a broad class of stationary black holes, including rotating and non-spherical cases, under specific convergence conditions.

Findings

Absorption cross section equals horizon area at zero frequency.

Zero-frequency scattering cross section vanishes.

Equality holds for stationary black holes with vanishing expansion.

Abstract

We discuss the absorption cross section for the minimally-coupled massless scalar field into a stationary and circularly symmetric black hole with nonzero angular velocity in four or higher dimensions. In particular, we show that it equals the horizon area in the zero-frequency limit provided that the solution of the scalar field equation with an incident monochromatic plane wave converges pointwise to a smooth time-independent solution outside the black hole and on the future horizon, with the error term being at most linear in the frequency. We also show that this equality holds for static black holes which are not necessarily spherically symmetric. The zero-frequency scattering cross section is found to vanish in both cases. It is shown in an Addendum that the equality holds for any stationary black hole with vanishing expansion if the limit solution is known to be a constant.