42,600 research outputs found
The Cardy-Verlinde Formula and Charged Topological AdS Black Holes
We consider the brane universe in the bulk background of the charged
topological AdS black holes. The evolution of the brane universe is described
by the Friedmann equations for a flat or an open FRW-universe containing
radiation and stiff matter. We find that the temperature and entropy of the
dual CFT are simply expressed in terms of the Hubble parameter and its time
derivative, and the Friedmann equations coincide with thermodynamic formulas of
the dual CFT at the moment when the brane crosses the black hole horizon. We
obtain the generalized Cardy-Verlinde formula for the CFT with an R-charge, for
any values of the curvature parameter k in the Friedmann equations.Comment: 10 pages, LaTeX, references adde
A Tight Karp-Lipton Collapse Result in Bounded Arithmetic
Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems
Hawking Radiation as a Mechanism for Inflation
The Friedman-Robertson-Walker (FRW) space-time exhibits particle creation
similar to Hawking radiation of a black hole. In this essay we show that this
FRW Hawking radiation leads to an effective negative pressure fluid which can
drive an inflationary period of exponential expansion in the early Universe.
Since the Hawking temperature of the FRW space-time decreases as the Universe
expands this mechanism naturally turns off and the inflationary stage
transitions to a power law expansion associated with an ordinary radiation
dominated Universe.Comment: 6 pages. Published version -- Awarded "Honorable Mention" for the
2012 Gravity Research Foundation Essay Contes
Thermodynamic of the Ghost Dark Energy Universe
Recently, the vacuum energy of the QCD ghost in a time-dependent background
is proposed as a kind of dark energy candidate to explain the acceleration of
the Universe. In this model, the energy density of the dark energy is
proportional to the Hubble parameter , which is the Hawking temperature on
the Hubble horizon of the Friedmann-Robertson-Walker (FRW) Universe. In this
paper, we generalized this model and choice the Hawking temperature on the
so-called trapping horizon, which will coincides with the Hubble temperature in
the context of flat FRW Universe dominated by the dark energy component. We
study the thermodynamics of Universe with this kind of dark energy and find
that the entropy-area relation is modified, namely, there is an another new
term besides the area term.Comment: 8 pages, no figure
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
FPTAS for Weighted Fibonacci Gates and Its Applications
Fibonacci gate problems have severed as computation primitives to solve other
problems by holographic algorithm and play an important role in the dichotomy
of exact counting for Holant and CSP frameworks. We generalize them to weighted
cases and allow each vertex function to have different parameters, which is a
much boarder family and #P-hard for exactly counting. We design a fully
polynomial-time approximation scheme (FPTAS) for this generalization by
correlation decay technique. This is the first deterministic FPTAS for
approximate counting in the general Holant framework without a degree bound. We
also formally introduce holographic reduction in the study of approximate
counting and these weighted Fibonacci gate problems serve as computation
primitives for approximate counting. Under holographic reduction, we obtain
FPTAS for other Holant problems and spin problems. One important application is
developing an FPTAS for a large range of ferromagnetic two-state spin systems.
This is the first deterministic FPTAS in the ferromagnetic range for two-state
spin systems without a degree bound. Besides these algorithms, we also develop
several new tools and techniques to establish the correlation decay property,
which are applicable in other problems
Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model
In Verlinde's entropic force scenario of gravity, Newton's laws and Einstein
equations can be obtained from the first pinciples and general assumptions.
However, the equipartition law of energy is invalid at very low temperatures.
We show clearly that the threshold of the equipartition law of energy is
related with horizon of the universe. Thus, a one-dimension Debye (ODD) model
in the direction of radius of the modified entropic force (MEF) maybe suitable
in description of the accelerated expanding universe. We present a Friedmann
cosmic dynamical model in the ODD-MEF framework. We examine carefully
constraints on the ODD-MEF model from the Union2 compilation of the Supernova
Cosmology Project (SCP) collaboration, the data from the observation of the
large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe
Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the
model parameters and , with
. The corresponding age of the universe agrees with the
result of D. Spergel {\it et al.}\cite{Spergel2003} at 95% confidence level.
The numerical result also yields an accelerated expanding universe without
invoking any kind of dark energy. Taking as a
running parameter associated with the structure scale , we obtain a possible
unified scenario of the asymptotic flatness of the radial velocity dispersion
of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11
anomaly in the entropic force framework of Verlinde.Comment: 23 pages, 6 figure
Notes on Matter in Horava-Lifshitz Gravity
We investigate the dynamics of a scalar field governed by the Lifshitz-type
action which should appear naturally in Horava-Lifshitz gravity. The wave of
the scalar field may propagate with any speed without an upper bound. To
preserve the causality, the action cannot have a generic form. Due to the
superluminal propagation, a formation of a singularity may cause the breakdown
of the predictability of the theory. To check whether such a catastrophe could
occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It
turns out that the dust does not collapse completely to form a singularity in a
generic situation, but expands again after it attains a maximum energy density.Comment: 14 pages, references adde
- …