AdS4 black holes with nonlinear source in rainbow gravity

We explore new four-dimensional black holes, with the Einstein-Lambda theory coupled to nonlinear electrodynamics, in an energy-dependent spacetime. By considering the power-law model of nonlinear electrodynamics and solving the coupled field equations, with properly fixing the parameters of the theory, we obtain two new classes of nonlinearly charged black holes with anti-de Sitter (AdS) asymptote. With the aim of studying the thermodynamic properties of the novel AdS black holes, we calculate the conserved and thermodynamic quantities such as black hole mass, electric charge, electric potential, temperature, and entropy in the presence of rainbow functions. Although some of these quantities are affected by the rainbow functions, interestingly, they satisfy the first law of black hole thermodynamics in its standard form. Based on the canonical ensemble method and by calculating the black hole heat capacity, we analyze the black hole local stability or thermodynamic phase transitions. The horizon radius of those black holes which experience type one or type two phase transition as well as the conditions under which the black holes remain stable are determined. Finally, via consideration of black hole thermal fluctuations, we examine the impacts of quantum gravitational corrections on the thermodynamic properties of our new AdS rainbow black holes. (C) 2019 The Author(s). Published by Elsevier B.V.