Advanced Methods in Black-Hole Perturbation Theory

TL;DR

This paper reviews advanced analytical methods for studying small perturbations around stationary black holes, highlighting recent extensions and open problems in the field.

Contribution

It introduces new extensions of semianalytical techniques for solving linearized field equations in black-hole perturbation theory.

Findings

Enhanced methods for linear perturbation analysis

Pedagogical explanations of current techniques

Identification of open problems in the field

Abstract

Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved spacetime. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.