Abstract
Abstract In this paper, we consider a massless field, with spin j, in interaction with a Schwarzschild black hole in four dimensions, focusing mainly our study on the s-wave scattering. First, using a Fourier analysis, we show that one can have a simple and natural description of the Physics near the event horizon without using any conformal field approaches. Then, within the same “scattering picture”, we derive analytically the imaginary part of the highly damped quasinormal complex frequencies and, as a natural consequence of our analysis, we show that thermal effects and in particular Hawking radiation, can be understood through the scattering of an ingoing s-wave by the non null barrier of the Regge-Wheeler potential associated with the Schwarzschild black hole. Finally, with the help of the well-known expression of the highly damped quasinormal complex frequencies, we propose a heuristic extension of the “tripled Pauli statistics” suggested by Motl, some years ago.
Highlights
Complex frequencies of the corresponding BH, beyond the leading order term
Within the same “scattering picture”, we derive analytically the imaginary part of the highly damped quasinormal complex frequencies and, as a natural consequence of our analysis, we show that thermal effects and in particular Hawking radiation, can be understood through the scattering of an ingoing s-wave by the non null barrier of the Regge-Wheeler potential associated with the Schwarzschild black hole
The Hawking radiation and thermal effects for a Schwarzschild BH are associated with the scattering of the s-waves by the “l = 0” Regge-Wheeler potential barrier
Summary
We consider first a static spherically symmetric four-dimensional spacetime with metric ds. It should be noted that a metric such as (2.1) does not describe the most general static spherically symmetric spacetime but it will permit us to apply the following results to the Schwarzschild case. We would like to refer the reader to [3] for a d-dimensional generalization of the scattering of a massless scalar field by a static and spherically symmetric BH through the semi-classical CAM techniques. We recall that the S-matrix elements, noted Sl(ω), are related to the reflection amplitude by It has been shown in [2,3,4] (and references therein) that the S-matrix permits to analyze the resonant aspects of the considered BH as well as to construct the form factor describing the scattering of a monochromatic scalar wave.
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