Calculation of, and bounds for, the multipole moments of stationary spacetimes

TL;DR

This paper simplifies the calculation of multipole moments in stationary spacetimes by replacing tensor recursion with scalar recursion and provides bounds, confirming part of a longstanding conjecture.

Contribution

It introduces a scalar recursion method for multipole moments and establishes bounds, advancing understanding of Geroch's conjecture.

Findings

Scalar recursion replaces tensor recursion for multipole moments

Bounds are established for the multipole moments

Proof of the necessary part of Geroch's conjecture

Abstract

In this paper the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on R^2. We also give a bound on the multipole moments. This gives a proof of the "necessary part" of a long standing conjecture due to Geroch.