The collision of two slowly rotating, initially non boosted, black holes in the close limit

TL;DR

This paper models the collision of two slowly rotating, non-boosted black holes in close proximity, using perturbation theory and numerical evolution to analyze gravitational wave emission and angular momentum transfer.

Contribution

It introduces an extension of the Regge-Wheeler-Zerilli perturbation framework to higher orders for evolving black hole collisions with rotation.

Findings

Quantitative estimates of gravitational wave energy emitted.

Analysis of angular momentum transfer during collision.

Validation of perturbation approach for slow rotation cases.

Abstract

We study the collision of two slowly rotating, initially non boosted, black holes in the close limit. A ``punctures'' modification of the Bowen - York method is used to construct conformally flat initial data appropriate to the problem. We keep only the lowest nontrivial orders capable of giving rise to radiation of both gravitational energy and angular momentum. We show that even with these simplifications an extension to higher orders of the linear Regge-Wheeler-Zerilli black hole perturbation theory, is required to deal with the evolution equations of the leading contributing multipoles. This extension is derived, together with appropriate extensions of the Regge-Wheeler and Zerilli equations. The data is numerically evolved using these equations, to obtain the asymptotic gravitational wave forms and amplitudes. Expressions for the radiated gravitational energy and angular momentum are derived and used together with the results of the numerical evolution to provide quantitative expressions for the relative contribution of different terms, and their significance is analyzed.