Thermodynamics and quantum tunneling of Reissner–Nordström black holes with deficit solid angle and quintessence

We study thermodynamics and quantum tunneling of the Reissner–Nordström black hole with deficit solid angle and quintessence. We employ black hole thermodynamical laws and Parikh–Wilczek’s semiclassical tunneling process to obtain expressions of some thermodynamics quantities, Boltzmann factor, and entropy variation of the black hole. Regarding black hole background as dynamical and using conservation laws for energy and charge, we detect the existence of unthermal radiation spectrum and dependence of Boltzmann factor on the background geometry, and on energy and charge of the radiant particle. We explicitly plot variations of temperature, heat capacity, Boltzmann factor, and entropy change for various values of deficit solid angle [Formula: see text] and quintessence density [Formula: see text]. When varying the black hole entropy, there exists a phase transition, which shifts to lower entropy for increasing [Formula: see text] and decreasing [Formula: see text]. We show that temperature, heat capacity, and quantum tunneling rate are decreased in presence of quintessence and deficit angle parameters.

f(T,R) theory of gravity

We mainly focus on the idea that the dynamics of the whole universe may be understood by making use of torsion [Formula: see text] and curvature [Formula: see text] at the same time. The [Formula: see text]-gravity can be considered as a fundamental gravitational theory describing the evolution of the universe. The model can produce the unification of the general relativity (GR), teleparallel gravity (TPG), [Formula: see text]-gravity and [Formula: see text]-gravity theories. For this purpose, the corresponding Lagrangian density is written in terms of an arbitrary function of the torsion and curvature scalars. Furthermore, we use the absence/existence puzzle of relativistic neutron stars and thermodynamical laws as constraining tools for the new proposal.

A thermodynamical analysis of the inhomogeneous FLRW type model: Redefined Bekenstein–Hawking system

A detailed thermodynamical study has been presented for the inhomogeneous FLRW-type model of the Universe bounded by a horizon with three possible modifications of Bekenstein–Hawking formulation of thermodynamical parameters namely entropy and temperature. For the first choice of the thermodynamical system validity of both the first law of thermodynamics (FLT) and the generalized second law of thermodynamics (GSLT) are examined. Also, the integrability conditions for the exact one-forms in both the thermodynamical laws are analyzed and it is found that they are consistent with each other. On the other hand, for the other two choices of the thermodynamical system to hold the first law of thermodynamics, one must restrict the parameters (in the definition of the thermodynamical variables) in some specific integral form.

ENTROPY AND ITS QUANTUM THERMODYNAMICAL IMPLICATION FOR ANOMALOUS SPECTRAL SYSTEMS

The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases, it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region.

Brans–Dicke theory and thermodynamical laws on apparent and event horizons

In this work, we describe the Brans–Dicke (BD) theory of gravity and give a particular solution by choosing a power law form for the scalar field [Formula: see text] and constant ω. If we assume that the first law of thermodynamics and the entropy formula hold on the apparent horizon, then we recover the Friedmann equations. Next, assuming the first law of thermodynamics holds, the validity conditions of the generalized second law (GSL) on the event horizon are presented. If we impose the entropy relation on the horizon, without using the first law, then we also obtain the validity condition of the GSL on the event horizon. The validity of the GSL completely depends on the BD model scalar field solutions. We have justified that the two processes are equivalent on the apparent horizon, but on the event horizon they are not equivalent. If the first law is valid on the event horizon, then the GSL may be satisfied by the BD solution, but if the first law is not satisfied then the GSL is not satisfied by the BD solution. Therefore, the first law always favours the GSL on the event horizon. In our effective approach, the first law and the GSL are always satisfied on the apparent horizon, which does not depend on the BD theory of gravity.

THERMODYNAMICAL LAWS IN HOŘAVA–LIFSHITZ GRAVITY

In this work, we investigate the validity of the GSL of thermodynamics in the universe (open, closed and flat) governed by Hořava–Lifshitz (HL) gravity. If the universe contains barotropic fluid, we obtain the corresponding solutions. The validity of the GSL is examined by two approaches: (i) the robust approach and (ii) the effective approach. In the robust approach, we consider that the universe contains only matter fluid. Also, the effect of the gravitational sector of HL gravity is incorporated through the modified black hole entropy on the horizon. The effective approach is that all extra information of HL gravity is cast into an effective dark energy fluid, and so we consider that the universe contains matter fluid plus this effective fluid. This approach is essentially the same as Einstein's gravity theory. The general prescription for the validity of the GSL is discussed. Graphically, we show that the GSL may be satisfied for the open, closed and flat universes on the different horizons with different conditions.