Uniform electric field solutions in Einstein-Maxwell-Dilaton gravity

Abstract

We revisit static, spherically symmetric black hole solutions within the framework of Einstein-Maxwell-Dilaton (EMD) theory, assuming a constant (uniform) Maxwell invariant. By introducing an appropriate dilaton potential and solving the resulting coupled field equations, we obtain non-asymptotically flat (NAF) black hole spacetimes. Our analysis demonstrates that even under a uniform Maxwell invariant, the EMD theory remains fundamentally distinct from Einstein-Scalar (ES) theory. To highlight these distinctions, we examine both the thermodynamic properties of the solutions and the tidal forces acting on an infalling extended object. In particular, we identify characteristic features in the radial and angular tidal components near the horizon and singularity. The presence of the electric field shifts the radius at which radial compression transitions to stretching and alters the intensity of angular compression, underscoring the crucial role of non-minimal electromagnetic couplings in shaping the global geometry and physical behavior of the spacetime. These results contribute to a deeper understanding of NAF black holes in dilaton-modified gravity frameworks.