New exact solutions for charged dilaton black holes in Born-Infeld electrodynamics: thermodynamic analysis

Abstract

We present new exact analytical solutions for spherically symmetric charged black holes in (\(3+1\))-dimensional Einstein-dilaton gravity coupled to nonlinear Born-Infeld electrodynamics. The scalar dilaton field non-minimally coupled to the electromagnetic sector modifies the asymptotic structure of spacetime, resulting in geometries that are neither asymptotically flat nor AdS. We perform a complete analytical derivation of the metric and electromagnetic potential functions, and show that the curvature singularities are covered by event horizons, confirming their black hole nature. Thermodynamic quantities, including mass, entropy, temperature, and electric potential, are derived through geometric and conserved charge methods. We verify that these solutions satisfy the first law of black hole thermodynamics, \(dM=TdS+UdQ\). Furthermore, within the canonical ensemble, we analyze the heat capacity and find regions of thermodynamic stability and instability, with possible phase transitions depending on the dilaton and Born-Infeld parameters. These solutions extend known dilaton black hole configurations and provide new insights into the interplay between scalar fields, nonlinear electrodynamics, and black hole thermodynamics.