Thermodynamics of BTZ-type charged black holes in Bopp Podolsky electrodynamics

TL;DR

This paper investigates how Bopp Podolsky electrodynamics, a higher derivative extension of Maxwell's theory, influences the thermodynamics and geometry of charged BTZ black holes in (2+1) dimensions, revealing modifications to temperature and horizon structure.

Contribution

It introduces a perturbative analysis of charged BTZ black holes within Bopp Podolsky electrodynamics, highlighting the impact of the Bopp Podolsky parameter on black hole geometry and thermodynamics.

Findings

Bopp Podolsky parameter modifies black hole horizon structure.

Hawking temperature depends on Bopp Podolsky coupling and cosmological constant.

Thermodynamic behavior remains well-defined despite marginal energy condition violations.

Abstract

We tested the thermodynamic properties of charged BTZ-type black holes (BHs) in the framework of Bopp Podolsky electrodynamics, a higher derivative extension of Maxwells theory that preserves gauge invariance while introducing a massive photon mode. Using a perturbative approach, we derive first and second order corrections to the metric and electric field, revealing how the Bopp Podolsky parameter b modifies the geometry and horizon structure. Unlike in four dimensional illustrations, where such corrections can lead to wormhole solutions, the (2+1)dimensional case retains a black hole interpretation, albeit with curvature dependent deformations that vanish asymptotically. We compute the Hawking temperature via the Hamilton Jacobi tunneling method, demonstrating its dependence on both the cosmological constant and the Bopp Podolsky coupling. Our results indicate that while energy conditions are marginally violated for certain parameter regimes, the BHs thermodynamic behavior remains well-defined, with temperature corrections emerging from the interplay between higher derivative electrodynamics and the lower dimensional gravitational background.