Vacuum, ma non troppo: hidden matter distribution in symmetry-transformed electrovacuum spacetimes

TL;DR

This paper reveals that certain vacuum solutions in General Relativity, generated via symmetry transformations from electrovacuum spacetimes, actually contain hidden matter distributions when expressed in Weyl coordinates.

Contribution

It demonstrates that transformed vacuum solutions support hidden matter sources, specifically a semi-infinite annular mass distribution, which is not apparent in the original coordinates.

Findings

Transformed solutions are supported by a hidden matter distribution in Weyl form.

Equatorial null geodesics reach spatial infinity in finite affine parameter.

Hidden matter manifests as a semi-infinite annular mass in Weyl coordinates.

Abstract

We analyse two static spacetimes, recently generated from a Schwarzschild--Bertotti--Robinson electrovacuum seed through distinct symmetry transformations. The electromagnetic field of the transformed solutions can be set to zero and both solutions were presented as vacuum solutions of General Relativity. However, we show that once recast in Weyl form, both metrics are seen to be supported by a semi-infinite annular mass distribution on the equatorial plane. Thus, these metrics harbour a hidden matter source, visible in Weyl coordinates. In the original Schwarzschild-like coordinates equatorial null geodesics reach spatial infinity ($r\to\infty$) in finite affine parameter. In the Weyl representation, these geodesics approach the inner edge of the annulus, where the coordinate map degenerates.