217 research outputs found
Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
In this paper we revisit the relation between the Friedmann equations and the
first law of thermodynamics. We find that the unified first law firstly
proposed by Hayward to treat the "outer"trapping horizon of dynamical black
hole can be used to the apparent horizon (a kind of "inner" trapping horizon in
the context of the FRW cosmology) of the FRW universe. We discuss three kinds
of gravity theorties: Einstein theory, Lovelock thoery and scalar-tensor
theory. In Einstein theory, the first law of thermodynamics is always satisfied
on the apparent horizon. In Lovelock theory, treating the higher derivative
terms as an effective energy-momentum tensor, we find that this method can give
the same entropy formula for the apparent horizon as that of black hole
horizon. This implies that the Clausius relation holds for the Lovelock theory.
In scalar-tensor gravity, we find, by using the same procedure, the Clausius
relation no longer holds. This indicates that the apparent horizon of FRW
universe in the scalar-tensor gravity corresponds to a system of
non-equilibrium thermodynamics. We show this point by using the method
developed recently by Eling {\it et al.} for dealing with the gravity.Comment: v2: revtex, 23 pages, references added, minor changes, to appear in
PR
Thermodynamic Geometry and Critical Behavior of Black Holes
Based on the observations that there exists an analogy between the
Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black holes and the van der
Waals-Maxwell liquid-gas system, in which a correspondence of variables is
, we study the Ruppeiner geometry, defined as
Hessian matrix of black hole entropy with respect to the internal energy (not
the mass) of black hole and electric potential (angular velocity), for the RN,
Kerr and RN-AdS black holes. It is found that the geometry is curved and the
scalar curvature goes to negative infinity at the Davies' phase transition
point for the RN and Kerr black holes.
Our result for the RN-AdS black holes is also in good agreement with the one
about phase transition and its critical behavior in the literature.Comment: Revtex, 18 pages including 4 figure
Notes on Entropy Force in General Spherically Symmetric Spacetimes
In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton
gravity appears as an entropy force. In this paper we show how gravity appears
as entropy force in Einstein's equation of gravitational field in a general
spherically symmetric spacetime. We mainly focus on the trapping horizon of the
spacetime. We find that when matter fields are absent, the change of entropy
associated with the trapping horizon indeed can be identified with an entropy
force. When matter fields are present, we see that heat flux of matter fields
also leads to the change of entropy. Applying arguments made by Verlinde and
Smolin, respectively, to the trapping horizon, we find that the entropy force
is given by the surface gravity of the horizon. The cases in the untrapped
region of the spacetime are also discussed.Comment: revtex4, 21 pages, no figures, one reference added, published
version, to appear in Phys.Rev.
Holographic Superconductors with Ho\v{r}ava-Lifshitz Black Holes
We discuss the phase transition of planar black holes in Ho\v{r}ava-Lifshitz
gravity by introducing a Maxwell field and a complex scalar field. We calculate
the condensates of the charged operators in the dual CFTs when the mass square
of the complex scalar filed is and , respectively. We
compute the electrical conductivity of the \hl superconductor in the probe
approximation. In particular, it is found that there exists a spike in the
conductivity for the case of the operator with scaling dimension one. These
results are quite similar to those in the case of Schwarzschild-AdS black
holes, which demonstrates that the holographic superconductivity is a robust
phenomenon associated with asymptotic AdS black holes.Comment: 12 pages, 7 figures,refs adde
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
Thermodynamic Curvature of the BTZ Black Hole
Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black
hole are studied to get the effective dimension of its corresponding
statistical model. For this purpose, we make use of the geometrical approach to
the thermodynamics: Considering the black hole as a thermodynamic system with
two thermodynamic variables (the mass and the angular momemtum ), we
obtain two-dimensional Riemannian thermodynamic geometry described by positive
definite Ruppeiner metric. From the thermodynamic curvature we find that the
extremal limit is the critical point. The effective spatial dimension of the
statistical system corresponding to the near-extremal BTZ black holes is one.
Far from the extremal point, the effective dimension becomes less than one,
which leads to one possible speculation on the underlying structure for the
corresponding statistical model.Comment: 19 pages, LaTeX with revtex macro, 4 figures in eps file
Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and
bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual
holographic model has been constructed by coupling a pseudo scalar to the
gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this
paper, we investigate the non-relativistic fluid with Hall viscosity and curl
viscosity living on a finite radial cutoff surface in the bulk. Employing the
non-relativistic hydrodynamic expansion method, we obtain the incompressible
Navier-Stokes equations with Hall viscosity and curl viscosity. Unlike the
shear viscosity, the ratio of the Hall viscosity over entropy density is found
to be cutoff scale dependent, and it tends to zero when the cutoff surface
approaches to the horizon of the background spacetime.Comment: 22 pages, published versio
Generalized Misner-Sharp Energy in f(R) Gravity
We study generalized Misner-Sharp energy in gravity in a spherically
symmetric spacetime. We find that unlike the cases of Einstein gravity and
Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy
depends on a constraint condition in the gravity. When the constraint
condition is satisfied, one can define a generalized Misner-Sharp energy, but
it cannot always be written in an explicit quasi-local form. However, such a
form can be obtained in a FRW universe and for static spherically symmetric
solutions with constant scalar curvature. In the FRW universe, the generalized
Misner-Sharp energy is nothing but the total matter energy inside a sphere with
radius , which acts as the boundary of a finite region under consideration.
The case of scalar-tensor gravity is also briefly discussed.Comment: Revtex, 17 pages, v2: some references added, to appear in PR
Notes on Ghost Dark Energy
We study a phenomenological dark energy model which is rooted in the
Veneziano ghost of QCD. In this dark energy model, the energy density of dark
energy is proportional to Hubble parameter and the proportional coefficient is
of the order , where is the mass scale of QCD.
The universe has a de Sitter phase at late time and begins to accelerate at
redshift around . We also fit this model and give the
constraints on model parameters, with current observational data including
SnIa, BAO, CMB, BBN and Hubble parameter data. We find that the squared sound
speed of the dark energy is negative, which may cause an instability. We also
study the cosmological evolution of the dark energy with interaction with cold
dark matter.Comment: 20 pages,10 figures,Correct some typos and add new reference
Cardy-Verlinde Formula and AdS Black Holes
In a recent paper hep-th/0008140 by E. Verlinde, an interesting formula has
been put forward, which relates the entropy of a conformal formal field in
arbitrary dimensions to its total energy and Casimir energy. This formula has
been shown to hold for the conformal field theories that have AdS duals in the
cases of AdS Schwarzschild black holes and AdS Kerr black holes. In this paper
we further check this formula with various black holes with AdS asymptotics.
For the hyperbolic AdS black holes, the Cardy-Verlinde formula is found to hold
if we choose the ``massless'' black hole as the ground state, but in this case,
the Casimir energy is negative. For the AdS Reissner-Nordstr\"om black holes in
arbitrary dimensions and charged black holes in D=5, D=4, and D=7 maximally
supersymmetric gauged supergravities, the Cardy-Verlinde formula holds as well,
but a proper internal energy which corresponds to the mass of supersymmetric
backgrounds must be subtracted from the total energy. It is failed to rewrite
the entropy of corresponding conformal field theories in terms of the
Cardy-Verlinde formula for the AdS black holes in the Lovelock gravity.Comment: 18 pages, latex, no figures, discussions on the charged AdS black
holes change
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