Magnetic solutions in Einstein-massive gravity with linear and nonlinear fields

TL;DR

This paper explores magnetic solutions in Einstein-massive gravity coupled with linear and nonlinear electromagnetic fields, analyzing their geometric properties and how these generalizations affect the deficit angle and overall spacetime structure.

Contribution

It introduces new magnetic solutions in Einstein-massive gravity with nonlinear electromagnetic fields, highlighting their geometric features and the impact on deficit angles in different backgrounds.

Findings

Solutions are free of curvature singularity but have conic singularities.

The deficit angle is affected by the type of electromagnetic field and background spacetime.

Different effects are observed in AdS and dS spacetimes.

Abstract

The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The paper at hand investigates the geometrical properties of the magnetic solutions by considering Maxwell and power Maxwell invariant (PMI) nonlinear electromagnetic fields in the context of massive gravity. These solutions are free of curvature singularity, but have a conic one which leads to presence of deficit/surplus angle. The emphasize is on modifications that these generalizations impose on deficit angle which determines the total geometrical structure of the solutions, hence, physical/gravitational properties. It will be shown that depending on the background spacetime (being anti de Sitter (AdS) or de Sitter (dS)), these generalizations present different effects and modify the total structure of the solutions differently.