The Yamabe invariant for axially symmetric two Kerr black holes initial data

TL;DR

This paper constructs a specific initial data metric for two Kerr black holes with aligned angular momentum, proving its positive Yamabe invariant when the black holes are sufficiently separated, which is useful for modeling such systems.

Contribution

It provides an explicit conformal metric for two Kerr black holes with large separation and aligned spins, demonstrating positive Ricci scalar and Yamabe invariant.

Findings

The constructed metric has positive Ricci scalar when black holes are far apart.

The metric enables the creation of initial data for two Kerr black holes with large angular momentum.

The Yamabe invariant is positive for the constructed initial data at large separation.

Abstract

An explicit 3-dimensional Riemannian metric is constructed which can be interpreted as the (conformal) sum of two Kerr black holes with aligned angular momentum. When the separation distance between them is large we prove that this metric has positive Ricci scalar and hence positive Yamabe invariant. This metric can be used to construct axially symmetric initial data for two Kerr black holes with large angular momentum.