Black hole collisions: how far can perturbation theory go?

TL;DR

This paper reviews recent progress in perturbation theory for rotating black holes, aiming to extend its applicability to larger separations and improve gravitational waveform predictions for black hole mergers.

Contribution

It discusses the development of second order perturbation theory around Kerr black holes to enhance the close limit approximation's validity.

Findings

Progress in modeling perturbations around Kerr black holes.

Potential to extend perturbation theory to larger black hole separations.

Advancement towards more accurate gravitational wave templates.

Abstract

The computation of gravitational radiation generated by the coalescence of inspiralling binary black holes is nowdays one of the main goals of numerical relativity. Perturbation theory has emerged as an ubiquitous tool for all those dynamical evolutions where the two black holes start close enough to each other, to be treated as single distorted black hole (close limit approximation), providing at the same time useful benchmarks for full numerical simulations. Here we summarize the most recent developments to study evolutions of perturbations around rotating (Kerr) black holes. The final aim is to generalize the close limit approximation to the most general case of two rotating black holes in orbit around each other, and thus provide reliable templates for the gravitational waveforms in this regime. For this reason it has become very important to know if these predictions can actually be trusted to larger separation parameters (even in the region where the holes have distinct event horizons). The only way to extend the range of validity of the linear approximation is to develop the theory of second order perturbations around a Kerr hole, by generalizing the Teukolsky formalism.