Thermal fluctuations of AdS black holes in three-dimensional rainbow gravity

• Published in: Physics letters. B Vol. 793; pp. 234 - 239
• Main Author: Dehghani, M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 10-06-2019; Elsevier
• Subjects: Nonlinear electrodynamics; Thermal fluctuations; Three-dimensional black hole; Thermal fluctuations; Three-dimensional black hole; Nonlinear electrodynamics
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2019.04.058

In this work, we explore the charged black holes with the power-law modified electromagnetic theory in a three-dimensional energy dependent space-time. Through exact solution of the field equations, we introduce a new class of nonlinearly charged black holes which are asymptotically anti-de Sitter (AdS). The black hole entropy, temperature and electric potential are calculated from the geometrical approaches. The counterterm method and Gauss's electric law are utilized for calculating the black hole mass and electric charge, respectively. By use of the Smarr formula, which states the black hole mass as the function of thermodynamic extensive parameters, we prove the validity of the first law of thermodynamics for the new AdS black holes. By use of the canonical ensemble method, the black hole remnant or phase transitions are investigated regarding the signature of black hole heat capacity. We show that the AdS black hole solutions, we just obtained, are thermodynamically stable if their horizon radii are greater than a minimum value. Then, by considering the black hole thermal fluctuations, we examine the quantum gravitational effects on the thermodynamic properties of the new AdS black holes. We prove that, when the thermal fluctuations are taken into account, the thermodynamical first law is no longer valid. Also, the thermal stability of the black holes gets some corrections.