Construction of N-body time-symmetric initial data sets in general relativity

TL;DR

This paper develops a method to construct N-body initial data sets in general relativity by creating a Riemannian manifold with zero scalar curvature that models multiple gravitational bodies in a time-symmetric state.

Contribution

It introduces a novel construction technique for N-body initial data sets with prescribed boundary neighborhoods in the context of general relativity.

Findings

Successfully constructs initial data sets modeling multiple bodies

Provides a new approach for solving the Einstein constraint equations

Enables better modeling of gravitational systems in initial data form

Abstract

Given a collection of N asymptotically Euclidean ends with zero scalar curvature, we construct a Riemannian manifold with zero scalar curvature and one asymptotically Euclidean end, whose boundary has a neighborhood isometric to the disjoint union of a specified collection of sub-regions of the given ends. An application is the construction of time-symmetric solutions of the constraint equations which model N-body initial data.