Colliding black holes: how far can the close approximation go?

TL;DR

This paper advances the understanding of black hole collisions by applying second-order perturbation theory, improving waveform accuracy and establishing the method's validity range for gravitational wave modeling.

Contribution

It introduces second-order perturbation theory to better model black hole collisions, providing error estimates and enhancing the utility of perturbation methods for gravitational wave research.

Findings

Second-order results align more closely with numerical simulations.

Perturbation theory's validity range is clarified.

Provides benchmarks for numerical relativity and waveform templates.

Abstract

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed waveforms and energy. Much more important, second-order results correctly indicate the range of validity of perturbation theory. This use of second-order, to provide ``error bars,'' makes perturbation theory a viable tool for providing benchmarks for numerical relativity in more generic collisions and, in some range of collision parameters, for supplying waveform templates for gravitational wave detection.