Perturbations and Stability of Static Black Holes in Higher Dimensions

Understand

In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case.

• We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of (m+n)-dimensional spacetimes with a warped product metric, including black hole geometry.
• We classify perturbations of such a background into three types, the tensor, vector and scalar-type, according to their tensorial behaviour on the n-dimensional part of the background spacetime, and for each type of perturbations, we introduce a set of manifestly gauge invariant variables.
• We then introduce harmonic tensors and write down the equations of motion for the expansion coefficients of the gauge invariant perturbation variables in terms of the harmonics.