Fine structure of high-energy absorption cross sections for black holes

TL;DR

This paper investigates the detailed structure of high-energy absorption cross sections for black holes, revealing a fine and hyperfine structure beyond the eikonal approximation through analytical and numerical methods.

Contribution

It introduces an analytical description of the fine structure of black hole absorption cross sections using Regge pole techniques, extending the analysis to various static spherically symmetric black holes.

Findings

Identification of a simple fine structure in the absorption cross section

Analytical expression for the fine structure using Regge poles

Observation of a hyperfine structure beyond the fine structure

Abstract

The high-energy absorption cross section of the Schwarzschild black hole is well approximated, in the eikonal regime, by the sum of two terms: the geometrical cross section of the black hole photon sphere and the contribution of a sinc function involving the geometrical characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on this photon sphere. From a numerical analysis, we show that, beyond the eikonal description, this absorption cross section presents a simple fine structure. We then describe it analytically by using Regge pole techniques and interpret it in geometrical terms. We naturally extend our analysis to arbitrary static spherically symmetric black holes endowed with a photon sphere and we then apply our formalism to Schwarzschild-Tangherlini and Reissner-Nordstr\"om black holes. Finally, on the example of the Schwarzschild black hole, we show numerically that a complicated hyperfine structure lying beyond the fine structure can also be observed.