On thermal fluctuations and quantum regularities of $\mathcal{F}(R,\mathcal{G})$ gravity black holes with constant topological Euler density in nonlinear electrodynamics

TL;DR

This paper investigates the thermodynamics, stability, and quantum regularity of topological black holes in $\\mathcal{F}(R,\mathcal{G})$ gravity coupled with nonlinear electrodynamics, revealing conditions under which singularities are quantum mechanically regular.

Contribution

It introduces a detailed analysis of thermodynamical properties, stability, and quantum regularity of black holes in modified gravity with nonlinear electrodynamics, including logarithmic entropy corrections.

Findings

Black holes exhibit stable thermodynamic behavior under certain conditions.

Quantum probes suggest naked singularities can be quantum mechanically regular.

Logarithmic entropy corrections influence thermodynamical variables and stability.

Abstract

We discuss the corrected thermodynamics and naked singularity structure of the topological static spherically symmetric solution in $\mathcal{F}(R,\mathcal{G})$ - gravity coupled with Born-Infeld - like nonlinear electrodynamics. Solutions admitting black holes with constant topological Euler density is analyzed in view of various thermodynamical variables. The inclusion of logarithmic correction to the entropy is extended to the other thermodynamical variables and the contribution of corrected variables are displayed on various plots. The stability of black hole under the effect of thermal variables is also studied. As a second scope of this study, solutions admitting timelike naked singularity are probed with bosonic and fermionic quantum wave packets to see if the singularity is quantum mechanically regular or not. In this context, the evolution of these probes remains well-defined if the corresponding spatial Hamiltonian operator is essentially self-adjoint. Our calculations reveal that when the singularity is probed with specific wave modes involving spin - $0$ and spin - $1/2$ quantum wave packets, the corresponding wave operators turn out to be essentially self-adjoint, which in turn implies unique well-defined time evolution.