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Register a new userThermodynamics of charged AdS black holes in rainbow gravity
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In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including (P) and (r)) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge (Q). Furthermore, we study the Gibbs function and find its characteristic swallow tail behavior, which indicates the phase transition. We also find there is a special value about the mass of test particle which would lead the black hole to zero temperature and a diverging heat capacity with a fixed charge.
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In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated.
We study topological black hole solutions of the simplest quadratic gravity action and we find that two classes are allowed. The first is asymptotically flat and mimics the Reissner-Nordstrom solution, while the second is asymptotically de Sitter or anti-de Sitter. In both classes, the geometry of the horizon can be spherical, toroidal or hyperbolic. We focus in particular on the thermodynamical properties of the asymptotically anti-de Sitter solutions and we compute the entropy and the internal energy with Euclidean methods. We find that the entropy is positive-definite for all horizon geometries and this allows to formulate a consistent generalized first law of black hole thermodynamics, which keeps in account the presence of two arbitrary parameters in the solution. The two-dimensional thermodynamical state space is fully characterized by the underlying scale invariance of the action and it has the structure of a projective space. We find a kind of duality between black holes and other objects with the same entropy in the state space. We briefly discuss the extension of our results to more general quadratic actions.
Treating the cosmological constant as a dynamical variable, we investigate the thermodynamics and weak cosmic censorship conjecture (WCCC) of a charged AdS black hole (BH) in the Rastall gravity. We determine the energy momentum relation of charged fermion at the horizon of the BH by using the Dirac equation. Based on this relation, we show that the first law of thermodynamics (FLT) still holds as a fermion is absorbed by the BH. However, the entropy of both the extremal and near-extremal BH decreases in the irreversible process, which means that the second law of thermodynamics (SLT) is violated. Furthermore, we verify the validity of the WCCC by the minimum values of the metric function h(r) at its final state. For the extremal charged AdS BH in the Rastall gravity, we find that the WCCC is valid always since the BH is extreme. While for the case of near-extremal BH, we find the WCCC could be violable in the extended phase space (EPS), depending on the value of the parameters of the BH and their variations.
We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of CS coupling constant beyond its supergravity amount, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and do not manifest uniquely by their global charges.
In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes $R_Nt^2$ and $K_Nt$ are calculated with the temperature parameter $t=T/T_c-1$ where $T_c$ the critical value of the temperature. Near the critical point, we find that the critical amplitude of $R_Nt^2$ and $K_Nt$ is $-frac{1}{2}$ when $trightarrow0^+$, whereas $R_Nt^2approx -frac{1}{8}$ and $K_Ntapprox-frac{1}{4}$ in the limit $trightarrow0^-$. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.
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