Scalar-Electromagnetic Couplings as Source of Deformed Black Hole: From Shadows to Thermodynamic Topology

TL;DR

This paper constructs a new black hole solution supported by nonlinear electrodynamics and a scalar field, analyzing its horizon, shadow, thermodynamics, and topological properties, and comparing with observational data from the Event Horizon Telescope.

Contribution

It introduces a one-parameter family of electromagnetic Lagrangians coupled to a scalar field, linking theoretical models to observational constraints and topological classifications.

Findings

Determines the critical magnetic charge for horizon formation.

Calculates shadow radius constrained by Event Horizon Telescope data.

Shows the thermodynamic behavior includes a Hawking-Page transition without van der Waals criticality.

Abstract

We reconstruct a static and spherically symmetric black hole geometry originally proposed as an effective metric by identifying a consistent matter source derived from a fundamental action. The space-time is supported by a magnetically charged nonlinear electrodynamics (NED) field non-minimally coupled to a scalar field. Dimensional consistency reduces the parameter space to a single magnetic charge, and the inverse construction formalism yields a one-parameter family of electromagnetic Lagrangians $\mathcal{L}(F)=F^{n+1}/(n+1)$, encompassing both linear and nonlinear electrodynamics. We analyze the horizon structure and determine the critical magnetic charge separating black hole and horizonless configurations. The photon sphere and the corresponding shadow radius are computed, and observational bounds from the Event Horizon Telescope for Sagittarius A* constrain the allowed range of the magnetic charge. In the extended phase space thermodynamics, the solution satisfies the first law and the Smarr relation, exhibits a Hawking-Page phase transition, and presents a single change in stability without van der Waals-type critical behavior. We also investigate the topological properties of both the photon sphere and the thermodynamic parameter space. The photon sphere carries a total topological charge $Q_{\text{tot}}=-1$, while the thermodynamic vector field yields a global winding number $W=0$, placing the solution in the same topological class as the one of the Reissner-Nordstr\"om black hole. We finally discuss the versatility of this non-minimal coupling framework in both providing theoretical support to previously introduced solution and also to connect them to observational settings within strong-field gravity.