Conformal classes of asymptotically flat, static vacuum data

TL;DR

This paper characterizes specific asymptotically flat, static vacuum data that are conformally rescalable, revealing they must be axi-symmetric with a conformal Killing field, and identifies a three-parameter family of such data.

Contribution

It proves that conformally rescalable, asymptotically flat, static vacuum data are necessarily axi-symmetric and possess a conformal Killing field, and it establishes the existence of a three-parameter family of these data.

Findings

Data must be axi-symmetric with a conformal Killing field.

Existence of a 3-parameter family of such data.

Conformal rescaling preserves asymptotic flatness and static vacuum conditions.

Abstract

We show that time-reflection symmetric, asymptotically flat, static vacuum data which admit a non-trivial conformal rescaling which leads again to such data must be axi-symmetric and admit a conformal Killing field. Moreover, it is shown that there exists a 3-parameter family of such data.