Nonminimal black holes with regular electric field

TL;DR

This paper explores how nonminimal coupling constants in Einstein-Maxwell theory can be unified into a single parameter, using exact solutions of regular black holes with electric fields to identify the domain of nonminimal interactions.

Contribution

It introduces a method to reduce three nonminimal coupling constants to one guiding parameter, the nonminimal radius, based on exact solutions with regular electric fields and metrics.

Findings

Nonminimal coupling constants can be unified into a single parameter.

The nonminimal radius marks the domain where nonminimal interactions dominate.

Exact solutions reveal the significance of the inflexion point in the metric function.

Abstract

We discuss the problem of identification of coupling constants, which describe interactions between photons and space-time curvature, using exact regular solutions to the extended equations of the nonminimal Einstein-Maxwell theory. We argue the idea that three nonminimal coupling constants in this theory can be reduced to the single guiding parameter, which plays the role of nonminimal radius. We base our consideration on two examples of exact solutions obtained earlier in our works: the first of them describes a nonminimal spherically symmetric object (star or black hole) with regular radial electric field; the second example represents a nonminimal Dirac-type object (monopole or black hole) with regular metric. We demonstrate that one of the inflexion points of the regular metric function identifies a specific nonminimal radius, thus marking the domain of dominance of nonminimal interactions.