Aspects of linearized perturbations of black holes and flat black strings

Abstract

This thesis presents a study in aspects of linearized perturbations of flat black strings and black holes in D dimensions. Main focus of the thesis is on analysis the non-spherically symmetric perturbations of these objects. We have formulated simplified equations for the non-spherically symmetric scalar and vector perturbations and explored the large D limit of general relativity as an analytical tool to study them. Using these equations, we have studied stability of flat black string and semiclassical stability of black holes in the path integral formulation of Euclidean quantum gravity in D-dimensions. Analyzing classical stability of flat black strings, we proved that the non-spherically symmetric perturbations do not lead to Gregory-Laflamme type instability. As the classical stability of D-dimensional black string is related to semiclassical stability of (D − 1)-dimensional black hole, this analysis also proves that the Gross-Perry-Yaffe negative mode is the unique semiclassically unstable mode of the Schwarzschild-Tangherlini black holes. We have computed, for the first time, quasinormal modes of D-dimensional black strings under non-spherically symmetric perturbations. We have calculated frequencies of O(1) (called decoupled mode frequencies) and those of order O(D) (non-decoupled mode frequencies) to various orders in D for vector perturbations of these objects. We have also re-analyzed quasinormal modes of Schwarzschild-Tangherlini black holes in the large D limit, with a different approach from previous works on this topic, by not assuming a 1/D expansion of the mode functions. We have studied semiclassical stability of the of D-dimensional Schwarzschild AdS black holes under both non-spherically symmetric and spherically symmetric (` = 0) perturbations. We have shown in various cases that the non-spherically symmetric perturbations do not lead to instability. In the case of spherically symmetric perturbations, where there is an instability, we have calculated eigenvalue corresponding to the unstable mode to next to leading order in D. We show that ix SYNOPSIS x the large black holes are stable but the small black holes are semiclassically unstable. This instability mimics features of thermodynamic (in)stability of (small) large black holes found by Hawking and Page.