Absorption cross section in gravity's rainbow from confluent Heun equation

TL;DR

This paper derives an asymptotic expression for the low-energy absorption cross section of a scalar field scattering off a charged black hole within gravity's rainbow framework, utilizing confluent Heun equations and advanced mathematical tools.

Contribution

It introduces a novel analytical approach combining confluent Heun equations and conformal blocks to compute black hole scattering properties in gravity's rainbow.

Findings

Derived an asymptotic formula for absorption cross section

Connected confluent Heun solutions with conformal blocks and Nekrasov-Shatashvili free energy

Provides insights into black hole scattering in modified gravity theories

Abstract

We investigate the scattering of a massless scalar field by a charged non-rotating black hole in the presence of gravity's rainbow. Using the connection coefficients of the confluent Heun equation expressed in terms of the semi-classical confluent conformal blocks and the instanton part of the Nekrasov-Shatashvili (NS) free energy, we obtain an asymptotic expansion for the low-energy absorption cross section.