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.
