Schwarzschild black-hole immersed in an electric or magnetic background in Entangled Relativity

TL;DR

This paper presents the first exact neutral Schwarzschild black-hole solutions in Entangled Relativity immersed in electric or magnetic backgrounds, showing their relation to General Relativity solutions and implications for astrophysical black-holes.

Contribution

It introduces the first neutral black-hole solutions in Entangled Relativity, expanding the theory's solution space beyond charged black-holes.

Findings

Black-hole solutions are neutral and exact in Entangled Relativity.

Schwarzschild solution emerges as a limit when background field vanishes.

Astrophysical black-holes in Entangled Relativity are similar to those in General Relativity.

Abstract

In this paper, we present the solution for a Schwarzschild black-hole immersed in an electric or magnetic background field \`a la Melvin within the framework of Entangled Relativity. Previous solutions in Entangled Relativity required black-holes to be charged for the matter field to be defined everywhere. This is because the theory precludes the existence of vacuum solutions, thereby satisfying Einstein's definition of Mach's Principle. The current black-hole solutions represent the first exact and neutral black-hole solutions of Entangled Relativity discovered to date. The Schwarzschild black-hole of General Relativity emerges as a limit of these solutions when the background field approaches zero, whereas the Melvin solution of General Relativity does not emerge as a limit when the black hole's size approaches zero. This finding suggests that astrophysical black-holes in Entangled Relativity are indistinguishable from those in General Relativity, given the generally weak interstellar density of matter fields.