Geodesics, Scalar Fields, and GUP-Corrected Thermodynamics of Charged BTZ-like Black Holes in Bopp-Podolsky Electrodynamics

TL;DR

This paper explores the effects of Bopp-Podolsky electrodynamics and GUP corrections on the properties and dynamics of charged BTZ-like black holes in (2+1) dimensions, including geodesics, scalar fields, and thermodynamics.

Contribution

It provides a detailed analysis of photon and scalar field dynamics, and introduces GUP-corrected Hawking temperature for charged BTZ-like black holes with topological defects.

Findings

Photon orbits are influenced by charge and topological defects.

Scalar wave propagation reveals potential barriers affected by electromagnetic and topological parameters.

GUP leads to suppressed Hawking radiation and possible stable black hole remnants.

Abstract

In Ref. [1], the spacetime geometry generated by compact objects in $(2+1)$-dimensional Bopp-Podolsky electrodynamics is derived. Using a perturbative approach, the authors derived a charged BTZ-like black hole solution and computed corrections up to second order in a perturbative expansion valid far from the horizon. In this work, we investigate the same circularly symmetric three-dimensional charged BH solution pierced by disclinations. We begin by analyzing the motion of photons within this spacetime, focusing on how the geometric parameters influence the effective potential governing null geodesic motion. The corresponding equations of motion are derived, and the resulting orbital dynamics are explored through graphical methods to show the influence of key parameters including the BH mass $M$, electric charge $Q$, cosmological constant $\Lambda$, and BP coupling parameter $b^2$. Extending our analysis to wave dynamics, we examine the propagation of massless scalar fields in the BH solution by solving the Klein-Gordon equation. Through suitable coordinate transformations, we derive a Schr\"odinger-like equation with an effective potential that encodes the influence of the topological defect and electromagnetic corrections. Additionally, we investigate quantum gravitational effects by applying the Generalized Uncertainty Principle (GUP) to derive a GUP-corrected Hawking temperature, revealing systematic suppression of thermal radiation that could lead to stable BH remnants. Finally, we compute Keplerian frequencies for circular orbits, demonstrating how the interplay between charge, nonlinear electrodynamics, and disclination parameters creates distinctive observational signatures that could potentially test modified gravity theories in strong-field regimes.