Born-Infeld Electrogravity and Dyonic Black Holes

TL;DR

This paper introduces Born-Infeld electrogravity, coupling gravity and electromagnetism in a single framework, and analyzes dyonic black hole solutions, revealing unique extremal black hole properties in the small-charge limit.

Contribution

It formulates a unified Born-Infeld electrogravity theory using Palatini formalism and explores its black hole solutions and thermodynamics, highlighting novel extremal black hole features.

Findings

Derived field equations in Palatini formalism with Einstein-like gravity

Identified two interpretations of electrodynamics within the theory

Discovered a fundamental extremal black hole in the small-charge limit

Abstract

Born-Infeld electrogravity is defined through a Lagrangian that couples gravity and electromagnetism within a single determinantal structure. The field equations are derived in Palatini's formalism, where the metric, connection, and vector potential are varied independently in the action. As a result, the gravitational sector reduces to Einstein's equations with a torsion-free, metric-compatible connection. The electrodynamic sector, in turn, admits two equivalent interpretations or $pictures$: it can be seen either as a standard Born-Infeld electrodynamics in an effective background geometry, or as an $anomalous$ Born-Infeld electrodynamics in the physical metric. We illustrate the dynamics by analyzing the horizon structure, the extremality conditions, and the thermodynamics of spherically symmetric dyonic solutions. Remarkably, in the small-charge limit, Born--Infeld electrogravity admits a fundamental extremal black hole whose mass and horizon area are determined exclusively by the Born--Infeld and Newton constants and the speed of light.