Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy

TL;DR

This paper derives an exact black hole solution in higher-order curvature gravity coupled with ModMax electrodynamics and quintessence dark energy, analyzing thermodynamics, stability, phase transitions, and optical properties like shadows.

Contribution

It presents a new exact black hole solution incorporating higher-order curvature, nonlinear electrodynamics, and dark energy, with detailed thermodynamic and optical analyses.

Findings

Thermodynamic curvature divergences align with heat capacity zeros, indicating phase transitions.

Quintessence and higher-order curvature increase the black hole shadow size.

Electric charge reduces the shadow size, with quintessence having a more significant impact.

Abstract

In this work, we derive an exact black hole solution in higher-order curvature gravity by coupling an electromagnetic sector formulated within the ModMax framework to a quintessence dark energy component. Focusing on purely electrically charged configurations, we analyze the thermodynamic and geothermodynamic properties of the solution to investigate its stability and phase structure. Within this sector, the ModMax theory effectively reduces Maxwell electrodynamics up to a rescaling of the electric charge, and thus the obtained solution corresponds to a consistent subset of the broader nonlinear theory. Using thermodynamic geometry, we examine microscopic interactions and phase transitions, showing that divergences in the thermodynamic curvature coincide with the vanishing of the heat capacity, confirming the consistency of the phase structure. We further explore the optical properties of the black hole by studying null geodesics and determining the photon sphere and the corresponding shadow radius for different values of the quintessence state parameter $\omega$. Exact analytical expressions for the photon-sphere radius are derived, revealing that higher-order curvature corrections and quintessence significantly enhance the shadow size, whereas the electric charge has the opposite effect. Notably, quintessence is found to have a more pronounced impact on the shadow than the charge. These results highlight that dark energy and higher-order curvature corrections can yield potentially observable signatures in black hole shadows.