Exact static cylindrical solution to conformal Weyl gravity

We present the exact neutral black string solution in locally conformal invariant Weyl gravity. As a special case, the general relativity analogue still can be attained; however, only as a subfamily 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.