A New Method for Solving the Initial Value Problem with Application to Multiple Black Holes

TL;DR

This paper introduces a novel method for solving the initial value problem in general relativity, specifically for axisymmetric black hole configurations, improving upon existing approaches by better approximating Kerr black holes.

Contribution

The paper presents a new technique for constructing initial data in general relativity with axisymmetry, capable of approximating Kerr black holes more accurately than previous methods.

Findings

Method effectively models Kerr black holes in initial data

Produces more accurate black hole configurations at large separations

Improves upon Bowen-York initial data approach

Abstract

This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified components of the extrinsic curvature we solve for extrinsic curvature's remaining components. For the second part, after noting that initial data for the Kerr spacetime can be derived within our formalism we construct data for axisymmetric configurations of spinning black holes. Though our method is limited to axisymmetry, it offers an advantage over the Bowen-York proceedure that our data approach those for Kerr holes in the limit of large separations and in the close limit.