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

Abstract

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 value. 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 $O(\omega /M)$ correction to the Hawking spectrum.

17 pages, 1 figure, LaTex, typos corrected, one intermediate formula added

References in corpus (10)

• Tunnelling, Temperature and Taub-NUT Black Holes
• Tunnelling Methods and Hawking's radiation: achievements and prospects
• Temporal contribution to gravitational WKB-like calculations
• Hawking temperature from tunnelling formalism
• Problems with Tunneling of Thin Shells from Black Holes
• Reduced Hamiltonian for intersecting shells
• Reply to Comments on "Invariance of the tunneling method for dynamical black holes" arXiv:0907.2020
• The time factor in the semi-classical approach to the Hawking radiation
• Comment on the ``Invariance of the Tunneling Method for Dynamical Black Holes''
• Second comment to "Invariance of the tunneling method"