Born–Infeld electrogravity and dyonic black holes

Abstract Born–Infeld (BI) 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 BI electrodynamics in an effective background geometry, or as an anomalous BI 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.