The collision of boosted black holes: second order close limit calculations

TL;DR

This paper investigates head-on black hole collisions using second-order perturbation theory, extending previous work to include initial momentum and addressing subtle issues in higher-order calculations.

Contribution

It introduces second-order perturbation calculations for moving black holes starting from unsymmetrized data, improving accuracy and understanding of collision dynamics.

Findings

Second-order perturbation results agree well with expectations.

Increased initial momentum improves approximation accuracy.

The study highlights important issues in higher-order perturbation normalization.

Abstract

We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions.