Static spacetimes with prescribed multipole moments; a proof of a conjecture by Geroch

TL;DR

This paper proves Geroch's long-standing conjecture by providing sufficient conditions for the existence of static spacetimes with prescribed multipole moments and offers a constructive method to determine the metric.

Contribution

It establishes the sufficiency of conditions for static spacetimes with given multipole moments, completing Geroch's conjecture with a constructive proof.

Findings

Sufficient conditions for static spacetime existence with prescribed moments

Constructive method to compute the metric from moments

Confirmation that these conditions match known necessary conditions

Abstract

In this paper we give sufficient conditions on a sequence of multipole moments for a static spacetime to exist with precisely these moments. The proof is constructive in the sense that a metric having prescribed multipole moments up to a given order can be calculated. Since these sufficient conditions agree with already known necessary conditions, this completes the proof of a long standing conjecture due to Geroch.