Determinantal Born-Infeld Coupling of Gravity and Electromagnetism

TL;DR

This paper introduces a unified Born-Infeld inspired model coupling gravity and electromagnetism using a determinantal approach in a metric-affine framework, linking it to nonlinear electrodynamics and analyzing charged black hole solutions.

Contribution

It presents a novel determinantal formulation coupling gravity and electromagnetism, connecting it to Einstein-Hilbert and nonlinear electrodynamics, and explores black hole solutions.

Findings

Equations derived from the determinantal approach match those from Einstein-Hilbert plus nonlinear electrodynamics.

The model admits charged static black hole solutions.

The formulation bridges metric-affine and metric theories of gravity.

Abstract

We study a Born-Infeld inspired model of gravity and electromagnetism in which both types of fields are treated on an equal footing via a determinantal approach in a metric-affine formulation. Though this formulation is a priori in conflict with the postulates of metric theories of gravity, we find that the resulting equations can also be obtained from an action combining the Einstein-Hilbert action with a minimally coupled nonlinear electrodynamics. As an example, the dynamics is solved for the charged static black hole.