Aspherical Photon and Anti-Photon Surfaces

TL;DR

This paper identifies photon and anti-photon surfaces in non-spherically symmetric spacetimes, including solutions to Einstein and Einstein-Maxwell equations, revealing complex geometries beyond simple spherical symmetry.

Contribution

It demonstrates the existence of (anti-)photon surfaces in physically relevant, non-spherical spacetimes, expanding understanding of photon surface geometries.

Findings

Photon surfaces are not always spherical.

Examples include vacuum C-metric and Melvin solutions.

Lapse function varies in these spacetimes.

Abstract

In this note we identify photon surfaces and anti-photon surfaces in some physically interesting spacetimes, which are not spherically symmetric. All of our examples solve physically reasonable field equations, including for some cases the vacuum Einstein equations, albeit they are not asymptotically flat. Our examples include the vacuum C-metric, the Melvin solution of Einstein-Maxwell theory and generalisations including dilaton fields. The (anti-)photon surfaces are not round spheres, and the lapse function is not always constant.