Holographical Aspects of Dyonic Black Holes: Massive Gravity Generalization

The content of this paper includes studying holographical and thermodynamical aspects of dyonic black holes in the presence of massive gravity. For the first part of paper, thermodynamical properties of the bulk which includes black holes are studied and the main focus is on critical behavior. It will be shown that the existence of massive gravitons introduces remnant for temperature after evaporation of black holes, van der Waals phase transition for non‐spherical black holes and etc. The consistency of different thermodynamical approaches toward critical behavior of the black holes is presented and the physical properties near the region of thermal instability are given. Next part of the paper studies holographical aspects of the boundary theory. Magnetization and susceptibility of the boundary are extracted and the conditions for having diamagnetic and paramagnetic behaviors are investigated. It will be shown that generalization to massive gravity results into the existence of diamagnetic/paramagnetic phases in phase structure of the hyperbolic and horizon flat of boundary conformal field theory. Recent LIGO report of detecting the gravitational waves provided a deep insight to general relativity and existence of massive gravitons. Also, phase transition of black holes in analogy to the van der Waals gas/liquid system, opens a new theoretical avenue to study black hole thermodynamics. The effects of graviton's mass on thermodynamical structure of dyonic black holes and holographic properties of the corresponding conformal field theory are explored.