Charged Cylindrical Black Holes in Conformal Gravity

TL;DR

This paper introduces a new static charged black hole solution in conformal gravity with cylindrical topology, revealing two distinct solutions and a linear potential term that could impact particle motion.

Contribution

It presents the first static charged black hole solutions with cylindrical symmetry in conformal gravity, highlighting differences from Einstein's theory and the role of a linear potential term.

Findings

Two distinct solutions including a linear potential term

Recovery of the charged black string in Einstein's theory when a factor is zero

Potential implications for particle trajectories in conformal gravity

Abstract

Considering cylindrical topology we present the static solution for a charged black hole in conformal gravity. We show that unlike the general relativistic case there are two different solutions, both including a factor that when set to zero recovers the familiar static charged black string solution in Einstein's theory. This factor gives rise to a linear term in the potential that also features in the neutral case and may have significant ramifications for particle trajectories.