  Motivated by providing preliminary steps to understand the conception of
quantum gravity, in this paper, we study the phase structure of a semiclassical
gravitational system. We investigate the stability conditions and phase
transition of charged black holes in massive gravity via canonical and
geometrical thermodynamic approaches. We point out the effects of massive
parameter on stability conditions of these black holes and show how massive
coefficients affect the phase transition points of these black holes. We also
study the effects of boundary topology on thermodynamical behavior of the
system. In addition, we give some arguments regarding the role of higher
dimensions and highlight the effect of the electric charge in thermodynamical
behavior. Then, we extend our study to geometrical thermodynamic approach and
show that it can be a successful method for studying the black hole phase
transition. At last, by employing the relation between thermodynamical pressure
and cosmological constant, critical behavior of the system and the effects of
different parameters on critical values are investigated.
