On the Construction of Time-Symmetric Black Hole Initial Data

TL;DR

This paper reviews the 3+1 formalism for Einstein's equations, focusing on time-symmetric initial data for multiple black holes, highlighting the influence of topology on such configurations.

Contribution

It provides a pedagogical overview of constructing time-symmetric black hole initial data, including explicit descriptions for two-hole configurations and the role of topology.

Findings

Explicit multi-black-hole initial data are presented.

The impact of topology on initial data is emphasized.

The 3+1-split formalism is clarified for pedagogical purposes.

Abstract

We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry. Multi-Black-Hole data are presented and more explicitly described in the case of two holes. The effect of different topologies is emphasized.