Black holes in massive Einstein-dilaton gravity

In this paper, we focus on massive Einstein-dilaton gravity including the coupling of dilaton scalar field to massive graviton terms, and then derive static and spherically symmetric solutions of dilatonic black holes in four dimensional spacetime. We find that the dilatonic black hole could possess two horizons (event and cosmological), extreme (Nariai) and naked singularity for the suitably fixed parameters. In addition, we investigate thermodynamic properties of these dilatonic black holes, and check the corresponding first law of black hole thermodynamics. Extending to the massive Einstein-dilaton gravity in high dimensions, we further obtain the dilatonic black hole solutions in $(d+1)$ dimensional spacetime.