Testing the AdS/CFT Correspondence Through Thermodynamic Geometry of Nonlinear Electrodynamics AdS Black Holes with Generalized Entropies

TL;DR

This paper explores the thermodynamic phase structure of nonlinear electrodynamics AdS black holes using various entropy frameworks, demonstrating how geometric methods reveal critical points and phase transitions consistent with holographic duality.

Contribution

It introduces a comprehensive analysis of black hole thermodynamics with generalized entropies and geometric methods, linking phase transitions to holographic dual CFT behavior.

Findings

Critical points align with temperature extrema and specific heat divergences.

GTD curvature singularities correspond to phase transition locations.

Kaniadakis entropy introduces an additional critical point in all systems.

Abstract

We investigate the thermodynamics and thermodynamic geometry of several Anti--de Sitter black hole solutions arising from nonlinear electromagnetic theories, namely the ModMax, nonlinear electrodynamics (NED), and Euler--Heisenberg AdS black holes, together with their holographically dual conformal field theory (CFT) descriptions. The analysis is carried out within three entropy frameworks: the standard Bekenstein--Hawking entropy and the generalized R\'enyi and Kaniadakis entropies. For each system, we analyze the phase structure through the behavior of temperature, specific heat, and the scalar curvature obtained from geometrothermodynamics (GTD). We find that thermodynamic critical points correspond to extrema in the temperature--entropy relation and coincide with divergences of the specific heat. These locations are reproduced by singularities in the Legendre--invariant GTD curvature, demonstrating a consistent geometric interpretation of the phase transitions. A comparison between the bulk black hole systems and their dual CFT counterparts shows that the number and structure of critical points are preserved under the holographic correspondence. Our results further reveal that the Euler--Heisenberg AdS black hole exhibits a more intricate phase structure compared with the ModMax and NED cases, while the Kaniadakis entropy consistently generates an additional critical point across all systems considered. These findings highlight the combined influence of nonlinear electromagnetic dynamics and generalized entropy formalisms on the critical behavior of AdS black holes and their dual CFTs.