Magnetized vortex in three-dimensional $\mathrm{f(R)}$ gravity

TL;DR

This paper explores a three-dimensional black hole surrounded by Maxwell-Higgs vortices in $f(R)$ gravity, revealing a stable, ring-like magnetic structure with invariant temperature despite modifications to gravity.

Contribution

It demonstrates the existence of a ring-like BH-vortex system in $f(R)$ gravity with constant temperature, highlighting the influence of the black hole horizon on vortex structures.

Findings

Existence of a ring-like BH-vortex system with quantized magnetic flux.

Bekenstein-Hawking temperature remains constant regardless of vortex parameters.

Vortices are affected by the black hole horizon, forming cosmological magnetic rings.

Abstract

Modified Gravity Theories (MGTs) are extensions of General Relativity (GR) in its standard formulation. Therefore, within this framework, we will investigate a system composed of a black hole (BH) surrounded by Maxwell-Higgs vortices, forming the BH-vortex system. In the case of linear $f(R)$ gravity is adopted showing the existence of a three-dimensional ring-like BH-vortex system with quantized magnetic flux. Within this system, one notes the BH at $r=0$ and its event horizon at $r= r_0$, while the magnetic vortices are at $r \in (r_0, \infty)$. A remarkable result is the constancy of the Bekenstein-Hawking temperature ($T_H$), regardless of MGTs and vortex parameters. This invariance of $T_H$ suggests that the BH-vortex system reaches thermodynamic stability. Unlike the standard theory of Maxwell-Higgs vortices in flat spacetime, in $f(R)$ gravity, the vortices suffer the influence of the BH's event horizon. This interaction induces perturbations in the magnetic vortex profile, forming cosmological ring-like magnetic structures.