Thermodynamics of black holes in massive gravity with holography

For the black hole thermodynamics under the modified gravity model, there is a very controversial issue of whether coupling parameters can be treated as thermodynamic quantities. There is currently no clear consensus. In this study, we want to develop a criterion for this issue with the help of holography under the de Rham, Gabadadze and Tolley (dRGT) massive gravity theory. We find that the extensive properties of black hole thermodynamics can be used to constrain this issue and at this point, the black hole can also appear interesting thermodynamic phase transition. The proposal of the additive constraint may be applied to many other modified gravity models.