Energy-minimizing two black holes initial data

TL;DR

This paper investigates the construction of initial data for two black holes that minimizes the ADM mass, aiming to identify the most energetically favorable configuration for such a system.

Contribution

It introduces a method to analyze the variations of ADM mass and horizon areas, and demonstrates that Misner initial data do not achieve the minimal ADM mass.

Findings

Misner data do not minimize ADM mass

A new method for analyzing gravitational degrees of freedom

Identification of ground state initial data for two black holes

Abstract

An attempt to construct the ``ground state'' vacuum initial data for the gravitational field surrounding two black holes is presented. The ground state is defined as the gravitational initial data minimizing the ADM mass within the class of data for which the masses of the holes and their distance are fixed. To parameterize different geometric arrangements of the two holes (and, therefore, their distance) we use an appropriately chosen scale factor. A method for analyzing the variations of the ADM mass and the masses (areas) of the horizons in terms of gravitational degrees of freedom is proposed. The Misner initial data are analyzed in this context: it is shown that they do not minimize the ADM mass.