Graybody Factors and Infrared Divergences

A method of computing the gray-body factors for static spherically symmetric and BEC acoustic black holes using a Volterra integral equation is given. The results are used to investigate infrared divergences in the particle number, two-point function, point-split stress-energy tensor and density-density correlation function. Infrared divergences in the particle number and two-point function occur if the gray-body factor approaches a nonzero constant in the zero frequency limit, as happens for Schwarzschild-de Sitter black holes and BEC acoustic black holes. However, no infrared divergences occur in the point-split stress-energy tensor or the density-density correlation function.