Dilatonic black holes in dRGT massive gravity

Motivated by high interest in Lorentz invariant massive gravity models known as the dRGT massive gravity, we discuss the dRGT massive gravity including the coupling term between dilaton scalar field and massive graviton, and present static and spherically symmetric solutions of dilatonic black holes in four and higher dimensional spacetime. Later, we investigate phase structure of these black hole solutions, and discover that the dilatonic black hole could possess two horizons, extreme and naked singularity black holes for the suitably parameters values. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics.