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arXiv · 1501.01953

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

Paul R. Anderson·Alessandro Fabbri·Roberto Balbinot
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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.

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Paul R. Anderson, Alessandro Fabbri, Roberto Balbinot. 2015-01-08. Low frequency gray-body factors and infrared divergences: rigorous results. https://doi.org/10.1103/physrevd.91.064061

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