45 research outputs found
Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?
It is a common belief now that the explanation of the microscopic origin of
the Bekenstein-Hawking entropy of black holes should be available in quantum
gravity theory, whatever this theory will finally look like. Calculations of
the entropy of certain black holes in string theory do support this point of
view. In the last few years there also appeared a hope that an understanding of
black hole entropy may be possible even without knowing the details of quantum
gravity. The thermodynamics of black holes is a low energy phenomenon, so only
a few general features of the fundamental theory may be really important. The
aim of this review is to describe some of the proposals in this direction and
the results obtained.Comment: 38 page
Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities
Geometrical form of the one-loop divergences induced by conical singularities
of background manifolds is studied. To this aim the heat kernel asymptotic
expansion on spaces having the structure near
singular surface is analysed. Surface corrections to standard second
and third heat coefficients are obtained explicitly in terms of angle
of a cone and components of the Riemann tensor. These results are
compared to ones to be already known for some particular cases. Physical
aspects of the surface divergences are shortly discussed.Comment: preprint DSF-13/94, 13 pages, latex fil
Toroidal equilibria in spherical coordinates
The standard Grad-Shafranov equation for axisymmetric toroidal plasma
equilibrium is customary expressed in cylindrical coordinates with toroidal
contours, and through which benchmark equilibria are solved. An alternative
approach to cast the Grad-Shafranov equation in spherical coordinates is
presented. This equation, in spherical coordinates, is examined for toroidal
solutions to describe low Solovev and high plasma equilibria in
terms of elementary functions
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
Cones, Spins and Heat Kernels
The heat kernels of Laplacians for spin 1/2, 1, 3/2 and 2 fields, and the
asymptotic expansion of their traces are studied on manifolds with conical
singularities. The exact mode-by-mode analysis is carried out for 2-dimensional
domains and then extended to arbitrary dimensions. The corrections to the first
Schwinger-DeWitt coefficients in the trace expansion, due to conical
singularities, are found for all the above spins. The results for spins 1/2 and
1 resemble the scalar case. However, the heat kernels of the Lichnerowicz spin
2 operator and the spin 3/2 Laplacian show a new feature. When the conical
angle deficit vanishes the limiting values of these traces differ from the
corresponding values computed on the smooth manifold. The reason for the
discrepancy is breaking of the local translational isometries near a conical
singularity. As an application, the results are used to find the ultraviolet
divergences in the quantum corrections to the black hole entropy for all these
spins.Comment: latex file, 27 page