On a Static Solution to Einstein Equations with incoming and outgoing radiation

TL;DR

This paper presents a static, spherically symmetric solution to Einstein's equations with null radiation, revealing a naked singularity and potential interpretation as a mass envelope for static bodies, with implications for gravitational modeling.

Contribution

It introduces a novel static solution with null radiation that can serve as an envelope for more massive static spherical objects.

Findings

The solution features a naked singularity.

It is not asymptotically flat.

It can be interpreted as an envelope increasing the mass of static bodies.

Abstract

Einstein equations with $T_{\mu\nu} = k_\mu k_\nu + \ell_\mu \ell_\nu$ where $k, \ell$ are null are considered with spherical symmetry and staticity. The solution has naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.