Energy dependent topological Black holes in Massive gravity coupled to Double-Logarithmic Electrodynamics

Abstract

This paper is devoted to the study of nonlinear magnetically charged black holes in the context of massive gravity's rainbow. For this, a recently proposed model of double-Logarithmic electrodynamics has been coupled to massive gravity and the energy dependent static spherically symmetric line element is considered. New AdS black hole solutions in this set up are derived and the corresponding thermodynamical properties are discussed. The finite mass of the black hole and the associated thermodynamical quantities such as Hawking temperature and heat capacity have been computed. Furthermore, thermodynamical stability/instability and the possibility of thermal phase transitions are also investigated. The modified Smarr's relation has been derived and the first law of thermodynamics is also examined. It is also mentioned that the black hole solutions of massive gravity and gravity's rainbow can also be regained separately from our results with in this model of nonlinear electrodynamics.