Multipole Moments of Static Spacetimes

TL;DR

This paper reviews the development of multipole theory for static spacetimes, connecting potential theory, conformal geometry, and general relativity, aiming to motivate further mathematical research in this area.

Contribution

It consolidates and explains existing work on multipole moments in static spacetimes, highlighting open problems and encouraging mathematical exploration.

Findings

Summarizes key results in multipole theory for static spacetimes

Identifies open problems in the mathematical understanding of these multipole moments

Bridges potential theory, conformal geometry, and general relativity

Abstract

This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity, known to mathematicians and to perhaps motivate them to look at the open problems which still remain.