31,442 research outputs found
Horizon thermodynamics in fourth-order gravity
In the framework of horizon thermodynamics, the field equations of Einstein
gravity and some other second-order gravities can be rewritten as the
thermodynamic identity: . However, in order to construct the
horizon thermodynamics in higher-order gravity, we have to simplify the field
equations firstly. In this paper, we study the fourth-order gravity and convert
it to second-order gravity via a so-called " Legendre transformation " at the
cost of introducing two other fields besides the metric field. With this
simplified theory, we implement the conventional procedure in the construction
of the horizon thermodynamics in 3 and 4 dimensional spacetime. We find that
the field equations in the fourth-order gravity can also be written as the
thermodynamic identity. Moreover, we can use this approach to derive the same
black hole mass as that by other methods.Comment: 12 pages, no figur
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data
Effective identification of asymmetric and local features in images and other
data observed on multi-dimensional grids plays a critical role in a wide range
of applications including biomedical and natural image processing. Moreover,
the ever increasing amount of image data, in terms of both the resolution per
image and the number of images processed per application, requires algorithms
and methods for such applications to be computationally efficient. We develop a
new probabilistic framework for multi-dimensional data to overcome these
challenges through incorporating data adaptivity into discrete wavelet
transforms, thereby allowing them to adapt to the geometric structure of the
data while maintaining the linear computational scalability. By exploiting a
connection between the local directionality of wavelet transforms and recursive
dyadic partitioning on the grid points of the observation, we obtain the
desired adaptivity through adding to the traditional Bayesian wavelet
regression framework an additional layer of Bayesian modeling on the space of
recursive partitions over the grid points. We derive the corresponding
inference recipe in the form of a recursive representation of the exact
posterior, and develop a class of efficient recursive message passing
algorithms for achieving exact Bayesian inference with a computational
complexity linear in the resolution and sample size of the images. While our
framework is applicable to a range of problems including multi-dimensional
signal processing, compression, and structural learning, we illustrate its work
and evaluate its performance in the context of 2D and 3D image reconstruction
using real images from the ImageNet database. We also apply the framework to
analyze a data set from retinal optical coherence tomography
-dimensional regular black holes with nonlinear electrodynamics sources
On the basis of two requirements: the avoidance of the curvature singularity
and the Maxwell theory as the weak field limit of the nonlinear
electrodynamics, we find two restricted conditions on the metric function of
-dimensional regular black hole in general relativity coupled with
nonlinear electrodynamics sources. By the use of the two conditions, we obtain
a general approach to construct -dimensional regular black holes. In
this manner, we construct four -dimensional regular black holes as
examples. We also study the thermodynamic properties of the regular black holes
and verify the first law of black hole thermodynamics.Comment: 13 pages, 4 figures. in press in PL
Stability of black holes based on horizon thermodynamics
On the basis of horizon thermodynamics we study the thermodynamic stability
of black holes constructed in general relativity and Gauss-Bonnet gravity. In
the framework of horizon thermodynamics there are only five thermodynamic
variables . It is not necessary to consider concrete matter fields,
which may contribute to the pressure of black hole thermodynamic system. In
non-vacuum cases, we can derive the equation of state, . According to
the requirements of stable equilibrium in conventional thermodynamics, we start
from these thermodynamic variables to calculate the heat capacity at constant
pressure and Gibbs free energy and analyze the local and global thermodynamic
stability of black holes. It is shown that is the necessary condition for
black holes in general relativity to be thermodynamically stable, however this
condition cannot be satisfied by many black holes in general relativity. For
black hole in Gauss-Bonnet gravity negative pressure can be feasible, but only
local stable black hole exists in this case.Comment: 6 pages, 7 figure
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