Two black hole initial data

TL;DR

This paper presents compact formulae for Misner initial data describing two black holes with equal or unequal masses, analyzes their interaction energy, and discusses their properties in the context of initial data for numerical relativity.

Contribution

It provides explicit formulae for two-black-hole initial data with different mass configurations and analyzes their interaction energy in a specific limit.

Findings

Explicit formulae for equal and non-equal mass Misner data

Analysis of interaction energy in the Schwarzschild + test particle limit

Insights into the properties of two-black-hole initial data

Abstract

Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or non-equal masses (i.e. isometric or non-isometric horizons). The interaction energy in the "Schwarzschild + test particle" limit of the Misner data is analyzed.