Magnetized vortex in three-dimensional f(R) gravity

Departamento de Física, Universidade Federal do Ceará (UFC) - Campus do Pici, Fortaleza - CE, 60455-760, Brazil and Centro de Matématica, Computação e Cognição (CMCC), Universidade Federal do ABC (UFABC) Av. dos Estados 5001, CEP 09210-580, Santo André, São Paulo, Brazil

Received: 20 February 2026
Accepted: 2 April 2026

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 it 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 , while the magnetic vortices are at . 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.