Viscous Cosmology and Thermodynamics of Apparent Horizon

It is shown that the differential form of Friedmann equations of FRW universe can be recast as a similar form of the first law, $T_{h}dS_{h} = dE + WdV$, of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that the generalized second law of thermodynamics holds at the apparent horizon of FRW universe and preserves dominant energy condition.Comment: 8 page

Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In case of static metric of BTZ black hole, the field equations near horizon boundary can be expressed as a thermal identity $dE = TdS + P_{r}dA$, where $E = M$ is the mass of BTZ black hole, $dA$ is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, $P_{r}$ is the radial pressure provided by the source of Einstein equations, $S= 4\pi a$ is the entropy and $T = \kappa / 2\pi$ is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole and show that it is also possible to interpret the field equation near horizon as a thermodynamic identity $dE = TdS + P_{r}dA + \Omega_{+} dJ$, where $\Omega_{+}$ is the angular velocity and $J$ is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near horizon.Comment: 8 page

Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE

Thermodynamics of interacting entropy-corrected holographic dark energy in a non-flat FRW universe

A so-called "entropy-corrected holographic dark energy" (ECHDE), was recently proposed to explain the dark energy-dominated universe with the help of quantum corrections to the entropy-area relation in the setup of loop quantum cosmology. Using this new definition, we investigate its thermodynamical features including entropy and energy conservation. We describe the thermodynamical interpretation of the interaction between ECHDE and dark matter in a non-flat universe. We obtain a relation between the interaction term of the dark components and thermal fluctuation. Our study further generalizes the earlier works [M.R. Setare and E.C. Vagenas, Phys. Lett. B 666 (2008) 111; B. Wang et al., Phys. Lett. B 662 (2008) 1] in this direction.Comment: 14 pages, no figure, accepted by Int. J. Mod. Phys.

Deformation of Codimension-2 Surface and Horizon Thermodynamics

The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature of a spacelike hypersurface. In the more interesting case of codimension-2, after selecting a local null frame, this deformation equation reduces to the well known (cross) focusing equations. We show how the thermodynamics of trapping horizons is related to these deformation equations in two different formalisms: with and without introducing quasilocal energy. In the formalism with the quasilocal energy, the Hawking mass in four dimension is generalized to higher dimension, and it is found that the deformation of this energy inside a marginal surface can be also decomposed into the contributions from matter fields and gravitational radiation as in the four dimension. In the formalism without the quasilocal energy, we generalize the definition of slowly evolving future outer trapping horizons proposed by Booth to past trapping horizons. The dynamics of the trapping horizons in FLRW universe is given as an example. Especially, the slowly evolving past trapping horizon in the FLRW universe has close relation to the scenario of slow-roll inflation. Up to the second order of the slowly evolving parameter in this generalization, the temperature (surface gravity) associated with the slowly evolving trapping horizon in the FLRW universe is essentially the same as the one defined by using the quasilocal energy.Comment: Latex, 61 pages, no figures; v2, type errors corrected; v3, references and comments are added, English is improved, to appear in JHE

Thermodynamical properties of the Universe with dark energy

We have investigated the thermodynamical properties of the Universe with dark energy. Adopting the usual assumption in deriving the constant co-moving entropy density that the physical volume and the temperature are independent, we observed some strange thermodynamical behaviors. However, these strange behaviors disappeared if we consider the realistic situation that the physical volume and the temperature of the Universe are related. Based on the well known correspondence between the Friedmann equation and the first law of thermodynamics of the apparent horizon, we argued that the apparent horizon is the physical horizon in dealing with thermodynamics problems. We have concentrated on the volume of the Universe within the apparent horizon and considered that the Universe is in thermal equilibrium with the Hawking temperature on the apparent horizon. For dark energy with $w\ge -1$, the holographic principle and the generalized second law are always respected.Comment: two figures; v2: minor corrections and updates, JCAP in pres

Thermodynamics of apparent horizon and modified Friedman equations

Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum corrected relation, $S=\frac{A}{4G}-\alpha \ln \frac{A}{4G}+\beta \frac{4G}{A}$, we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.Comment: 11 page

Validity of Generalized Second Law of Thermodynamics in the Logamediate and Intermediate scenarios of the Universe

In this work, we have investigated the validity of the generalized second law of thermodynamics in logamediate and intermediate scenarios of the universe bounded by the Hubble, apparent, particle and event horizons using and without using first law of thermodynamics. We have observed that the GSL is valid for Hubble, apparent, particle and event horizons of the universe in the logamediate scenario of the universe using first law and without using first law. Similarly the GSL is valid for all horizons in the intermediate scenario of the universe using first law. Also in the intermediate scenario of the universe, the GSL is valid for Hubble, apparent and particle horizons but it breaks down whenever we consider the universe enveloped by the event horizon

The thermodynamic evolution of the cosmological event horizon

By manipulating the integral expression for the proper radius $R_e$ of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe, we obtain an analytical expression for the change \dd R_e in response to a uniform fluctuation \dd\rho in the average cosmic background density $\rho$. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that \dd\rho/\rho is constant. The respective variations 2\pi R_e \dd R_e and \dd E_e in the horizon entropy $S_e$ and enclosed energy $E_e$ should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature $T_e$ of the CEH at an arbitrary time in a flat FRW universe is $E_e/S_e$, which recovers asymptotically the usual static de Sitter temperature. Furthermore, it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T_e \drv S_e = P\drv V_e - \drv E_e, where $V_e$ is the enclosed volume and $P$ is the average cosmic pressure.Comment: 6 page