Kerr-Schild type initial data for black holes with angular momenta

TL;DR

This paper introduces a method to construct initial data for spinning black holes using Kerr-Schild superpositions, analyzes the close limit of oppositely spinning black holes, and computes gravitational radiation emitted during evolution.

Contribution

It presents a novel superposition technique for spinning black holes in Kerr-Schild coordinates and explicitly solves the constraint equations in the close limit.

Findings

Superposition satisfies physical limits including close and far regimes.

Explicit solutions for the constraint equations in the close limit.

Computed radiated energy as a function of black hole parameters.

Abstract

Generalizing previous work we propose how to superpose spinning black holes in a Kerr-Schild initial slice. This superposition satisfies several physically meaningful limits, including the close and the far ones. Further we consider the close limit of two black holes with opposite angular momenta and explicitly solve the constraint equations in this case. Evolving the resulting initial data with a linear code, we compute the radiated energy as a function of the masses and the angular momenta of the black holes.