COMPUTING THE SPECTRUM OF BLACK-HOLE RADIATION IN THE PRESENCE OF HIGH-FREQUENCY DISPERSION - AN ANALYTICAL APPROACH

We present a method for computing the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency disp ersion. The method involves a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations. The modified wave equation is obtained by adding a higher order derivative term suppressed by powers of a fundamental momentum s cale k(0) to the ordinary wave equation. Depending on the sign of this new term, high frequency modes propagate either superluminally or sub luminally. We show that the resulting spectrum of created particles is thermal at the Hawking temperature, and further that the out-state is a thermal state at the Hawking temperature, to leading order in k(0), for either modification.