Hairy black holes in Einstein-Weyl gravity

Higher derivative extensions of Einstein's general relativity are commonly viewed as alternative and effective theories of gravity, not just due to the fact that these arise naturally in the string theory approach to gravity, but mainly for their use in cosmology to generate geometric dark energy models. In a recent paper [Phys. Rev. Lett. 114, 171601 (2015)] Lu et al. used numerical methods to obtain static, spherically symmetric and asymptotically flat black hole solutions in vacuum Einstein-Weyl gravity and showed that these are different than the Schwarzschild black hole. Inspired by the absence of any no-hair theorem for Einstein-Weyl gravity, in this paper we derive numerical examples of black hole solutions with massive scalar hair, and study the effect of the scalar field on the black hole structure. We limit ourselves to static and spherically symmetric solutions which are asymptotically flat such that the scalar field is regular on the horizon and vanishes at infinity.