The stationary n-body problem in general relativity

TL;DR

This paper discusses the non-existence of certain stationary multi-body solutions in general relativity and compares these results with the Newtonian case, highlighting fundamental differences.

Contribution

It proves the non-existence of specific asymptotically flat, stationary solutions with multiple bodies in general relativity, extending previous results and providing detailed Newtonian analogs.

Findings

No such multi-body stationary solutions exist in general relativity under specified conditions.

The Newtonian case admits different solution structures, contrasting with the relativistic results.

The work clarifies the constraints imposed by spacetime symmetries on multi-body configurations.

Abstract

In this talk I describe recent joint works with R.Schoen and with G.Gibbons and R.Schoen which prove the non-existence of certain asymptotically flat, stationary solutions of the Einstein equations with more than one body. The basic restriction is for example satisfied when spacetime has an isometry reversing the sign of the timelike Killing vector and fixing a hypersurface in the space of Killing trajectories which is disjoint from the bodies. I also give a detailed treatment of the Newtonian situation.