Charged dilatonic black holes in dilaton-massive 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 charged dilatonic black holes in four dimensional spacetime. We find that the dilatonic black hole could possess different horizon structures for some suitably parameters. Then, we also investigate the thermodynamic properties of charged dilatonic black holes where $f(r)$ approaches $+\mathrm{\infty }$ and $-\mathrm{\infty }$, respectively.