Compact objects with scalar charge embedded in a magnetic or electric field in Einstein-Maxwell-dilaton theories

TL;DR

This paper extends the Schwarzschild-Melvin solution in Einstein-Maxwell-dilaton theories to include scalar charges and applies it to Entangled Relativity, confirming the accuracy of previous approximations for compact objects in zero-background fields.

Contribution

It generalizes the Schwarzschild-Melvin solution to include scalar charges and adapts it to Entangled Relativity, validating earlier approximations for neutron stars.

Findings

The generalized solution includes non-null scalar charges.

The solution confirms the approximation used in prior neutron star models.

Analytical solutions are consistent with exact solutions in zero-background fields.

Abstract

In this paper, we generalize the Schwarzschild-Melvin solution within Einstein-Maxwell-dilaton theories to include non-null scalar charges, while remaining embedded in a magnetic or electric field \textit{\`a la Melvin}. We then use this general solution to obtain the solution in the specific case of Entangled Relativity after a conformal transformation. This notably enables us to verify that the analytical solution used in [Arruga \& Minazzoli 2021] in order to represent compact objects such as neutron stars in Entangled Relativity is indeed a good approximation of the exact solutions of Entangled Relativity when the background field goes to zero.