Perturbations in the Kerr spacetime

Abstract

In the present dissertation we study s-spin weight field perturbations in the Kerr background. Such perturbations are described by an equation called Teukolsky master equation (TME). Here we show how to obtain the TME and study it. Then, in order to obtain the quasi-normal modes, that is, the possible frequencies of the field between the outer horizon and infinity, we discuss the continued fraction method (known as Leaver’s method in such context), which consists in writing a series expansion for the angular and radial equations derived from the TME. It follows that the coefficients of the series expansions obey a three-term recurrence relation (TTRR). For this reason, we study properties of TTRR to make clear the Leaver’s method, and then to obtain numerically the frequencies. In the last chapter we discuss the Kerr scattering problem and explain the Penrose process in order to make a link with black hole thermodynamics. Lastly, we address superradiance, which is directly related with the Hawking’s area theorem.