Radiating solutions in Entangled Relativity

TL;DR

This paper explores radiating solutions in Entangled Relativity, showing that Mineur--Vaidya solutions can be embedded in electromagnetic fields and that naked singularities can form dynamically, similar to General Relativity.

Contribution

It demonstrates the embedding of Mineur--Vaidya solutions in Entangled Relativity with electromagnetic fields and analyzes the formation of naked singularities within this framework.

Findings

Mineur--Vaidya solutions are valid in Entangled Relativity.

Naked singularities can form dynamically in this theory.

Solutions are consistent with Einstein--Maxwell--dilaton theories.

Abstract

The Mineur--Vaidya radiating solutions satisfy $\mathcal{L}_m ~\propto~ F^2 = 0 = R$. As a consequence, it is not only a solution in General Relativity, but also in Einstein--Maxwell--dilaton theories for all coupling constants. The specific case of Entangled Relativity is noteworthy because the additional scalar degree of freedom is defined from the ratio between $R$ and $\mathcal{L}_m$, which is ill-defined in this situation. In the present work, we embed the Mineur--Vaidya solution in a magnetic (or electric) field within the framework of Entangled Relativity, and show that the Mineur--Vaidya solution corresponds to the limit where the magnetic (respectively, electric) field vanishes. This notably allows us to demonstrate that, as in General Relativity, it is possible to dynamically form naked singularities in Entangled Relativity. This conclusion, in fact, applies to any Einstein--Maxwell--dilaton theory, although it does not seem to be widely acknowledged in the literature.