A scattering approach to some aspects of the Schwarzschild Black Hole

TL;DR

This paper analyzes s-wave scattering of a massless field by a Schwarzschild black hole, deriving quasinormal frequencies and explaining Hawking radiation through scattering, offering a new perspective without conformal field theory.

Contribution

It provides a simple scattering-based description of black hole physics near the horizon and analytically derives highly damped quasinormal modes, linking them to Hawking radiation.

Findings

Analytical expression for highly damped quasinormal frequencies.

Hawking radiation explained via scattering of ingoing s-waves.

Proposed extension of tripled Pauli statistics for black hole states.

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.