Families of conformally related asymptotically flat, static vacuum data

TL;DR

This paper classifies a 3-parameter family of asymptotically flat, static vacuum solutions that are conformally related, providing explicit forms using elliptic functions and revealing their conformal mappings.

Contribution

It extends previous work by fully describing conformally related static vacuum data, including explicit solutions and their conformal relationships.

Findings

Identifies a 3-parameter family of conformally related data

Provides explicit solutions using elliptic functions

Shows decomposition into conformal subclasses

Abstract

Extending the results of an earlier article we give a complete description of the asymptotically flat, conformally non-flat, static vacuum data which admit non-trivial, asymptotically smooth conformal mappings onto other such data. These data form a 3-parameter family which decomposes into 1-parameter families of data which are conformal to each other. The data and the associated static vacuum solutions are given explicitly in terms of elliptic and, in a special case, elementary functions.