Thermodynamics and orbital structure of anti-de Sitter black holes in Palatini-inspired nonlinear electrodynamics

TL;DR

This paper develops an anti-de Sitter black hole solution within Palatini-inspired nonlinear electrodynamics, analyzing its thermodynamics, geodesics, and optical properties, providing a foundation for further numerical and phenomenological research.

Contribution

It constructs the first exact AdS extension of the Palatini-inspired nonlinear electrodynamics black hole, preserving its structure and enabling detailed study of its properties.

Findings

Derived the full set of field equations for the AdS black hole solution.

Analyzed horizon structure, Hawking temperature, and thermodynamics.

Investigated geodesics, photon sphere, shadow radius, and stable orbits.

Abstract

We construct a consistent anti-de Sitter completion of the static and spherically symmetric black-hole solution sourced by the Palatini-inspired nonlinear electrodynamics \(Y^n\) model. Starting from the Einstein--Hilbert action with a negative cosmological constant and the first-order PINLED sector, we derive the full set of field equations and show that the nonlinear electromagnetic solution preserves its original parametric structure, while the lapse function acquires the standard AdS contribution. We then analyze the horizon structure, Hawking temperature, extended phase-space thermodynamics, and the associated equation of state. In addition, we investigate null and timelike geodesics, with emphasis on the effective potentials, photon sphere, shadow radius for a static observer at finite distance, and innermost stable circular orbit. The resulting framework furnishes the exact AdS extension of the asymptotically flat PINLED black hole and provides a coherent basis for numerical and phenomenological studies of its thermodynamic, optical, and orbital properties.