Solutions to the Reissner-Nordström, Kerr, and Kerr-Newman problems in fourth-order conformal Weyl gravity.

Abstract

We continue our study of the general structure of fourth-order conformal Weyl gravity which we are exploring as a possible theory of gravity, and in this paper we present three new exact solutions to the theory which we have found. First we present the complete and exact solution to the Reissner-Nordstr\"om problem associated with a static, spherically symmetric point electric and/or magnetic charge coupled to fourth-order conformal Weyl gravity. We find that, unlike the familiar second-order Einstein case where the modification to the Schwarzschild metric is in the form of a term which behaves like $\frac{1}{{r}^{2}}$, in the fourth-order case the modification is found to behave like $\frac{1}{r}$, i.e., just like the Newtonian potential term itself. Additionally, we present two further exact solutions to the theory which we have found, namely, those associated with the fourth-order Kerr and Kerr-Newman problems in which a stationary, axially symmetric rotating system with or without electric and/or magnetic charge is coupled to gravity.