  In this paper, we study the thermodynamics and geothermodynamics of spherical
black hole solutions in dRGT massive gravity in a new extended phase space.
Inspired by the work of Kastor et al. [1], by interpreting the graviton mass as
a thermodynamical variable, we propose a first law of thermodynamics which
include a mass term and establish a new Smarr Formula. Then, we perform a
thermodynamical analysis to reveal the existence of a critical behavior for
black holes in dRGT massive gravity with two different critical points through
canonical and grand canonical ensembles. To consolidate these results, we make
use of the thermodynamical geometry formalism, with the HPEM and the Gibbs free
energy metrics, to derive the singularities of Ricci scalar curvatures and show
that they coincide with those of the capacities. The effect of different values
of the spacetime parameters on the stability conditions is also discussed.

High Energy Physics - Theory