302 research outputs found
`Thermodynamics' of Minimal Surfaces and Entropic Origin of Gravity
Deformations of minimal surfaces lying in constant time slices in static
space-times are studied. An exact and universal formula for a change of the
area of a minimal surface under shifts of nearby point-like particles is found.
It allows one to introduce a local temperature on the surface and represent
variations of its area in a thermodynamical form by assuming that the entropy
in the Planck units equals the quarter of the area. These results provide a
strong support to a recent hypothesis that gravity has an entropic origin, the
minimal surfaces being a sort of holographic screens. The gravitational entropy
also acquires a definite physical meaning related to quantum entanglement of
fundamental degrees of freedom across the screen.Comment: 12 pages, 1 figur
Heat-kernel Coefficients and Spectra of the Vector Laplacians on Spherical Domains with Conical Singularities
The spherical domains with conical singularities are a convenient
arena for studying the properties of tensor Laplacians on arbitrary manifolds
with such a kind of singular points. In this paper the vector Laplacian on
is considered and its spectrum is calculated exactly for any
dimension . This enables one to find the Schwinger-DeWitt coefficients of
this operator by using the residues of the -function. In particular, the
second coefficient, defining the conformal anomaly, is explicitly calculated on
and its generalization to arbitrary manifolds is found. As an
application of this result, the standard renormalization of the one-loop
effective action of gauge fields is demonstrated to be sufficient to remove the
ultraviolet divergences up to the first order in the conical deficit angle.Comment: plain LaTeX, 23 pp., revised version, a misprint in expressions (1.8)
and (4.38) of the second heat coefficient for the vector Laplacian is
corrected. No other change
Radial geodesics as a microscopic origin of black hole entropy. I: Confined under the Schwarzschild horizon
Causal radial geodesics with a positive interval in the Schwarzschild metric
include a subset of trajectories completely confined under a horizon, which
compose a thermal statistical ensemble with the Hawking-Gibbons temperature.
The Bekenstein--Hawking entropy is given by an action at corresponding
geodesics of particles with a summed mass equal to that of black hole in the
limit of large mass.Comment: 16 pages, 12 eps-figures, iopart class, tought experiment (p.7) adde
Thermodynamics, Euclidean Gravity and Kaluza-Klein Reduction
The aim of this paper is to find out a correspondence between one-loop
effective action defined by means of path integral in Euclidean gravity
and the free energy obtained by summation over the modes. The analysis is
given for quantum fields on stationary space-times of a general form. For such
problems a convenient procedure of a "Wick rotation" from Euclidean to
Lorentzian theory becomes quite non-trivial implying transition from one real
section of a complexified space-time manifold to another. We formulate
conditions under which and can be connected and establish an explicit
relation of these functionals. Our results are based on the Kaluza-Klein method
which enables one to reduce the problem on a stationary space-time to
equivalent problem on a static space-time in the presence of a gauge
connection. As a by-product, we discover relation between the asymptotic
heat-kernel coefficients of elliptic operators on a dimensional stationary
space-times and the heat-kernel coefficients of a dimensional elliptic
operators with an Abelian gauge connection.Comment: latex file, 22 page
Thorny Spheres and Black Holes with Strings
We consider thorny spheres, that is 2-dimensional compact surfaces which are
everywhere locally isometric to a round sphere except for a finite number
of isolated points where they have conical singularities. We use thorny spheres
to generate, from a spherically symmetric solution of the Einstein equations,
new solutions which describe spacetimes pierced by an arbitrary number of
infinitely thin cosmic strings radially directed. Each string produces an angle
deficit proportional to its tension, while the metric outside the strings is a
locally spherically symmetric solution. We prove that there can be arbitrary
configurations of strings provided that the directions of the strings obey a
certain equilibrium condition. In general this equilibrium condition can be
written as a force-balance equation for string forces defined in a flat 3-space
in which the thorny sphere is isometrically embedded, or as a constraint on the
product of holonomies around strings in an alternative 3-space that is flat
except for the strings. In the case of small string tensions, the constraint
equation has the form of a linear relation between unit vectors directed along
the string axes.Comment: 37 pages, 11 figure
Thermodynamics and Statistical Mechanics of Induced Liouville Gravity
In this paper we describe a Liouville gravity which is induced by a set of
quantum fields (constituents) and represents a two-dimensional analog of
Sakharov's induced gravity. The important feature of the considered theory is
the presence of massless constituents which are responsible for the appearance
of the induced Liouville field. The role of the massive constituents is only to
induce the cosmological constant. We consider the instanton solutions of the
Euclidean Liouville gravity with negative and zero cosmological constants, some
instantons being interpreted as two-dimensional anti-de Sitter black
holes. We study thermodynamics of all the solutions and conclude that their
entropy is completely determined by the statistical-mechanical entropy of the
massless constituents. This shows, in particular, that the constituents of the
induced gravity are the true degrees of freedom of black holes. Special
attention is also paid to the induced Liouville gravity with zero cosmological
constant on a torus. We demonstrate the equivalence of its thermodynamics to
the thermodynamics of BTZ black holes and comment on computations of the BTZ
black hole entropy.Comment: 22 pages, latex, no figure
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