Exact Static Cylindrical Solution to Conformal Weyl Gravity

TL;DR

This paper derives an exact static cylindrically symmetric solution in conformal Weyl gravity, revealing a linear potential component that could impact astrophysical and microscopic phenomena.

Contribution

It provides the first exact exterior solution for a static, neutral cylindrically symmetric source in conformal Weyl gravity, including a linear potential term.

Findings

Solution reduces to general relativity in a special case

Linear potential grows over large distances

Potential implications for astrophysics and micro-scale physics

Abstract

We present the exact exterior solution for a static and neutral cylindrically symmetric source in locally conformal invariant Weyl gravity. As a special case the general relativity analogue still can be attained, however only as a sub-family of solutions. Our solution contains a linear term that would thus result in a potential that grows linearly over large distances. This may have implications for exotic astrophysical structures as well as matter fields on the extremely small scale.