In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the RN-AdS black hole surrounded by the quintessence under the scattering of a charged complex scalar field. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.
In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field. According to the energy and charge fluxes of the scalar field, the variations of this black hole’s energy and charge can be calculated during an infinitesimal time interval. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.
We investigate weak cosmic censorship conjecture in charged torus-like black hole by the complex scalar field scattering. Using the relation between the conserved quantities of a black hole and the scalar field, we can calculate the change of the energy and charge within the infinitesimal time. The change of the enthalpy is connected to the change of energy, then we use those results to test whether the first law, the second law as well as the weak cosmic censorship conjecture are valid. In the normal phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid, and the second law of thermodynamics is not violated. For the specific black hole under scalar field scattering we consider, in the extended phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid. However, the second law of thermodynamics is violated when the black hole’s initial charge reaches a certain value.
We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle, and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last, we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.
In this paper, we study the Joule–Thomson expansion for RN-AdS black holes immersed in perfect fluid dark matter. As perfect fluid dark matter is one of the dark matter candidates, we are interested in how it influences the thermodynamic properties of black holes. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity as the thermodynamic volume, which give us more physical insights into the black hole. Moreover, we derive the thermodynamic definitions and study the critical behaviour of the black hole. Secondly, the explicit expression of Joule–Thomson coefficient is obtained from the basic formulas of the pressure, the volume, the entropy and the temperature. Then, we obtain the inversion curves in terms of charge Q and parameter λ. Furthermore, we analyse the isenthalpic curve in T–P graph with the cooling–heating region determined by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and compare the result with that in the RN-AdS case.
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