Late-time expansion in the semiclassical theory of the Hawking radiation

Pietro Menotti
2012 Physical Review D  
We give a detailed treatment of the back-reaction effects on the Hawking spectrum in the late-time expansion within the semiclassical approach to the Hawking radiation. We find that the boundary value problem defining the action of the modes which are regular at the horizon admits in general the presence of caustics. We show that for radii less that a certain critical value r_c no caustic occurs for all values of the wave number and time and we give a rigorous lower bound on such a critical
more » ... e. We solve the exact system of non linear equations defining the motion, by an iterative procedure rigorously convergent at late times. The first two terms of such an expansion give the O(ω/M) correction to the Hawking spectrum.
doi:10.1103/physrevd.85.084005 fatcat:qvxdxwrj7vehrffjx62omfjz4e