Initial data for superposed rotating black holes

TL;DR

This paper introduces a new method for generating initial data for rotating black holes, especially Kerr black holes, using nonconformally flat geometries suitable for numerical simulations.

Contribution

It proposes a nonconformally flat 3-geometry approach for superposing Kerr black holes, improving initial data modeling for rotating black hole collisions.

Findings

Initial data solutions for Kerr black holes at large separation.

Initial data for rotating holes close enough to form a common horizon.

Demonstrates the feasibility of superposing Kerr holes with arbitrary mass and spin.

Abstract

The standard approach to initial data for both analytic and numerical computations of black hole collisions has been to use conformally-flat initial geometry. Among other advantages, this choice allows the simple superposition of holes with arbitrary mass, location and spin. The conformally flat restriction, however, is inappropriate to the study of Kerr holes, for which the standard constant-time slice is not conformally flat. Here we point out that for axisymmetric arrangements of rotating holes, a nonconformally flat form of the 3-geometry can be chosen which allows fairly simple superposition of Kerr holes with arbitrary mass and spin. We present initial data solutions representing locally Kerr holes at large separation, and representing rotating holes close enough so that outside a common horizon the spacetime geometry is a perturbation of a single Kerr hole.