Low frequency gray-body factors and infrared divergences: rigorous results

TL;DR

This paper rigorously derives low-frequency gray-body factors and analyzes infrared divergences for black holes and Bose-Einstein condensate acoustic black holes using integral equations, providing new analytic expressions and insights.

Contribution

It introduces a rigorous method to obtain analytic expressions for scattering coefficients and gray-body factors at zero frequency for black holes and BEC acoustic black holes.

Findings

Analytic expressions for zero-frequency gray-body factors

Insights into infrared divergences in two-point functions

Rigorous solutions for mode equations in black hole spacetimes

Abstract

Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a 1D Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.