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

Lovelock gravity from entropic force

In this paper, we first generalize the formulation of entropic gravity to (n+1)-dimensional spacetime. Then, we propose an entropic origin for Gauss-Bonnet gravity and more general Lovelock gravity in arbitrary dimensions. As a result, we are able to derive Newton's law of gravitation as well as the corresponding Friedmann equations in these gravity theories. This procedure naturally leads to a derivation of the higher dimensional gravitational coupling constant of Friedmann/Einstein equation which is in complete agreement with the results obtained by comparing the weak field limit of Einstein equation with Poisson equation in higher dimensions. Our study shows that the approach presented here is powerful enough to derive the gravitational field equations in any gravity theory. PACS: 04.20.Cv, 04.50.-h, 04.70.Dy.Comment: 10 pages, new versio

Fourth clivar workshop on the evaluation of ENSO processes in climate models: ENSO in a changing climate

n/aThe organizers acknowledge the generous support of the World Climate Research Programme/CLIVAR, the Centre National de la Recherche Scientifique–Institut National des Sciences de l’Univers (CNRS-INSU), the LabEx L-IPSL, and Sorbonne Universités and wish to thank Lei Han, from the International CLIVAR Global Project Office in Qingdao, China, for his invaluable help in organizing this workshop

Effects of Krill Oil on serum lipids of hyperlipidemic rats and human SW480 cells

© 2008 Zhu et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

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

On Charged Lifshitz Black Holes

We obtain exact solutions of charged asymptotically Lifshitz black holes in arbitrary (d+2) dimensions, generalizing the four dimensional solution investigated in 0908.2611[hep-th]. We find that both the conventional Hamiltonian approach and the recently proposed method for defining mass in non-relativistic backgrounds do not work for this specific example. Thus the mass of the black hole can only be determined by the first law of thermodynamics. We also obtain perturbative solutions in five-dimensional Gauss-Bonnet gravity. The ratio of shear viscosity over entropy density and the DC conductivity are calculated in the presence of Gauss-Bonnet corrections.Comment: 24 pages, no figures, to appear in JHE

Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory

We analyse in detail the thermodynamics in the canonical and grand canonical ensembles of a class of non-asymptotically flat black holes of the Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We present the first law of thermodynamics, the thermodynamic analysis of the system through the geometrothermodynamics methods, Weinhold, Ruppeiner, Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The geometric methods show a curvature scalar identically zero, which is incompatible with the results of the analysis made by the non null specific heat, which shows that the system is thermodynamically interacting, does not possess extreme case nor phase transition. We also analyse the local and global stability of the thermodynamic system, and obtain a local and global stability for the normal case for 0<\gamma<1 and for other values of \gamma, an unstable system. The solution where \gamma=0 separates the class of locally and globally stable solutions from the unstable ones.Comment: 18 pages, version accepted for publication in General Relativity and Gravitatio

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio

The holographic principle

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.Comment: 52 pages, 10 figures, invited review for Rev. Mod. Phys; v2: reference adde

Holographic Lovelock Gravities and Black Holes

We study holographic implications of Lovelock gravities in AdS spacetimes. For a generic Lovelock gravity in arbitrary spacetime dimensions we formulate the existence condition for asymptotically AdS black holes. We consider small fluctuations around these black holes and determine the constraint on Lovelock parameters by demanding causality of the boundary theory. For the case of cubic Lovelock gravity in seven spacetime dimensions we compute the holographic Weyl anomaly and determine the three point functions of the stress energy tensor in the boundary CFT. Remarkably, these correlators happen to satisfy the same relation as the one imposed by supersymmetry. We then compute the energy flux; requiring it to be positive is shown to be completely equivalent to requiring causality of the finite temperature CFT dual to the black hole. These constraints are not stringent enough to place any positive lower bound on the value of viscosity. Finally, we conjecture an expression for the energy flux valid for any Lovelock theory in arbitrary dimensions.Comment: 31 pages, 1 figure, harvmac, references added, calculation of viscosity/entropy ratio include