Analytical Quasinormal Modes of a Massless Scalar Field in Anti-de-Sitter Spacetimes with a Schwarzschild Black Hole

Abstract

The anti de Sitter black holes have recently become a popular research topic due to the correspondence between the theory of general relativity in the anti de Sitter spacetime and the conformal field theory, which gives us an opportunity to study a quantum system through a corresponding anti de Sitter (AdS) spacetime, containing black holes. In this work we study and analytically approximate the quasinormal modes of massless scalar wave in AdS spacetime, solutions to the wave equation, which satisfy the boundary conditions at the horizon and at distant region. The massless scalar wave at distant region exhibits some divergence. By choosing appropriate boundary conditions, not only the divergence is removed, but the qusinormal modes become polynomials their frequencies are discrete. Our analytical result is compared to the numerical result, which shows some similarity.