A scattering approach to some aspects of the Schwarzschild black hole

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.

Infinite statistics condensate as a model of dark matter

“…Dwarf galaxies have been already studied [20], these are dark matter dominated astrophysical objects with a very small contribution of baryons to the total matter content, which make them suitable for testing models of dark matter. Recently, the intermediate statistics is used in various aspects of gravitation and cosmology [21,22].…”

Scattering theory without large-distance asymptotics

“…By generalizing our result to tensor wave scattering, we can consider the scattering theory of gravitational waves, which has been studied under large-distance asymptotics in literature, e.g., [21,22]. Moreover, we can also consider the scattering of a wave scattered by a black hole; all discussions on this issue are based on large-distance asymptotics [23][24][25][26][27]. A relativistic scattering theory without large-distance asymptotics also can be established.…”

Scattering theory without large-distance asymptotics in arbitrary dimensions

“…[1] and the present paper can be also applied to scatterings of long-range potentials, which is usually studied under large-distance asymptotics [41]. In particular, we will discuss the scattering of a wave on a black hole in arbitrary dimensions, while research in literature is usually under large-distance asymptotics [42][43][44][45][46]. String theory related scatterings [47] can be also considered without large-distance asymptotics.…”