A Comprehensive Thermodynamic Study of the Reissner-Nordström-de Sitter Black Hole with a Constant Negative Curvature Surrounded by a Quintessence-like Anisotropic Fluid

Abstract The study investigates the thermodynamic characteristics of Reissner-Nordström black holes in the presence and absence of a quintessence-like fluid. We establish the relationships between key variables, such as mass, temperature, specific heat and Helmholtz free energy, in terms of entropy considering different scenarios. We also assess the value of the horizon radius for the second-order phase transition in the presence of a quintessence-like fluid. We also focus on the effects of logarithmic corrections in entropy, highlighting how these corrections cause the entropy ratio to deviate from unity. Moreover, we discuss the black hole’s equation of state, which serves as the foundation for deriving and plotting the temperature and P-V isotherm. In order to incorporate concepts like Planck’s length, we consider a generalized version of Heisenberg’s uncertainty principle and derive the constraints on the event horizon radius.