Construction of N-body initial data sets in general relativity

TL;DR

This paper presents a method to construct initial data sets for N-body problems in general relativity by combining solutions of the Einstein constraint equations, extending previous work to more general cases.

Contribution

It introduces a new construction technique for asymptotically Euclidean solutions of the Einstein constraints that include specified regions from multiple initial data sets.

Findings

Provides a systematic way to generate multi-body initial data in general relativity.

Extends previous time-symmetric constructions to more general cases.

Enables modeling of complex gravitational systems with multiple bodies.

Abstract

Given a collection of N solutions of the (3+1) vacuum Einstein constraint equations which are asymptotically Euclidean, we show how to construct a new solution of the constraints which is itself asymptotically Euclidean, and which contains specified sub-regions of each of the N given solutions. This generalizes earlier work which handled the time-symmetric case, thus providing a construction of large classes of initial data for the many body problem in general relativity.