Radiating solutions in Entangled Relativity

TL;DR

This work shows that Mineur–Vaidya radiating solutions, which in GR are known to yield singular and potentially naked singularities, can be embedded into Einstein–Maxwell–dilaton frameworks with magnetic or electric fields and then mapped into the Entangled Relativity (ER) frame. By constructing explicit Mineur–Vaidya–Melvin solutions in EM–dilaton theories and performing the inverse conformal transformation to ER, the authors demonstrate that ER admits radiating spacetimes with nonzero $R$ and $\mathcal{L}_m$, and that in the zero-field limit these reduce to the original MV solutions. The results show that naked singularities can form in Entangled Relativity just as in General Relativity, and this holds for all Einstein–Maxwell–dilaton couplings, providing a broad extension of the naked singularity literature. The analysis relies on geometric optics, conformal mappings between frames, and explicit expressions for the scalar $\vartheta=-\mathcal{L}_m/R$ and its electric/magnetic duals, highlighting the role of the non-linear $R$–$\mathcal{L}_m$ coupling in ER.

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.