Asymptotically flat black hole solutions in quadratic gravity

Abstract

Black holes constitute some of the most fascinating objects in our universe. According to Einstein’s theory of general relativity, they are also deceivingly simple: Schwarzschild black holes are completely determined by their mass. Moreover, the singularity theorems by Penrose and Hawking indicate that they host a curvature singularity within their event horizon. The presence of the latter invites the question whether these dead-end points of spacetime can be made regular by considering (quantum) corrections to the classical field equations. In this light, we use the Frobenius method to investigate the phase space of asymptotically flat, static, and spherically symmetric black hole solutions in quadratic gravity. We argue that the only asymptotically flat black hole solution visible in this approach is the Schwarzschild solution.