Topological Mod(A)Max AdS black holes

TL;DR

The paper constructs and analyzes topological AdS black holes in nonlinear ModMax and ModAMax electrodynamics, deriving the metric function and thermodynamic quantities within extended phase space. It demonstrates that ModMax can yield two horizons while ModAMax typically has a single horizon, and shows how the horizon topology k and the ModMax parameter γ govern temperatures, masses, and stability profiles. The work further examines Joule–Thomson expansion, inversion curves, and black-hole heat engine efficiencies, revealing that nonlinear electrodynamics and topology markedly influence thermodynamic performance and phase structure. These results illuminate the interplay between modified electrodynamics and spacetime topology in holographic contexts and suggest avenues for observational or phenomenological constraints on exotic matter couplings.

Abstract

In this work, we construct new classes of topological black hole solutions in anti-de Sitter (AdS) spacetime using a novel model of nonlinear electrodynamics called Modification Maxwell (ModMax) and Modification phantom or Modification anti-Maxwell (ModAMax). We then evaluate the thermodynamic quantities and verify the first law of thermodynamics. Our study examines how the parameters of the ModMax and ModAMax fields, as well as the topological constant, affect the black hole solutions, thermodynamic quantities, and local and global thermal stabilities. Furthermore, within the framework of extended phase space thermodynamics, we analyze the Joule-Thomson expansion process and determine the inversion curves. This analysis reveals that the ModMax and ModAMax parameters significantly alter the cooling and heating behavior of these AdS black holes, depending on their topology. Finally, by treating these topological Mod(A)Max AdS black holes as heat engines, we assess their efficiencies, demonstrating that the parameters of nonlinear electrodynamics and horizon topology play crucial roles in enhancing or suppressing the system's thermodynamic performance.

Figures (21)

• Figure 1: The metric function $f(r)$ versus $r$ for different values of the topological constant ($k$). Left panel for ModMax case ($\eta=+1$). Right panel for ModAMax or phantom case ($\eta=-1$).
• Figure 2: The metric function $f(r)$ versus $r$ for $k=+1$, and different values of the ModMax's parameter. Left panel for ModMax case ($\eta=+1$). Right panel for ModAMax or phantom case ($\eta=-1$).
• Figure 3: The metric function $f(r)$ versus $r$ for $k=0$, and different values of the ModMax's parameter. Left panel for ModMax case ($\eta=+1$). Right panel for ModAMax or phantom case ($\eta=-1$).
• Figure 4: The metric function $f(r)$ versus $r$ for $k=-1$, and different values of the ModMax's parameters. Left panel for ModMax case ($\eta=+1$). Right panel for ModAMax or phantom case ($\eta=-1$).
• Figure 5: The Hawking temperature $T$ versus $r_{+}$ for $k=+1$ (left panel), $k=0$ (middle panel), and $k=-1$ (right panel) by considering the ModMax field ($\eta =+1$).