865 research outputs found
The wave function of a gravitating shell
We have calculated a discrete spectrum and found an exact analytical solution
in the form of Meixner polynomials for the wave function of a thin gravitating
shell in the Reissner-Nordstrom geometry. We show that there is no extreme
state in the quantum spectrum of the gravitating shell, as in the case of
extreme black hole.Comment: 7 pages, 1 figur
Dynamics of a thin shell in the Reissner-Nordstrom metric
We describe the dynamics of a thin spherically symmetric gravitating shell in
the Reissner-Nordstrom metric of the electrically charged black hole. The
energy-momentum tensor of electrically neutral shell is modelled by the perfect
fluid with a polytropic equation of state. The motion of a shell is described
fully analytically in the particular case of the dust equation of state. We
construct the Carter-Penrose diagrams for the global geometry of the eternal
black hole, which illustrate all possible types of solutions for moving shell.
It is shown that for some specific range of initial parameters there are
possible the stable oscillating motion of the shell transferring it
consecutively in infinite series of internal universes. We demonstrate also
that this oscillating type of motion is possible for an arbitrary polytropic
equation of state on the shell.Comment: 17 pages, 7 figure
Generalized Taub-NUT metrics and Killing-Yano tensors
A necessary condition that a St\"ackel-Killing tensor of valence 2 be the
contracted product of a Killing-Yano tensor of valence 2 with itself is
re-derived for a Riemannian manifold. This condition is applied to the
generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It
is shown that in general the St\"ackel-Killing tensors involved in the
Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The
only exception is the original Taub-NUT metric.Comment: 14 pages, LaTeX. Final version to appear in J.Phys.A:Math.Ge
Path Integrals for Parastatistics
We demonstrate that parastatistics can be quantized using path integrals by
calculating the generating functionals for time-ordered products of both free
and interacting parabose and parafermi fields in terms of path integrals. We
also give a convenient form of the commutation relations for the Green
components of the parabose and parafermi operators in both the canonical and
path integral formalisms.Comment: typos corrected, references added, some new content. version that has
been publishe
Non-Extreme and Ultra-Extreme Domain Walls and Their Global Space-Times
Non-extreme walls (bubbles with two insides) and ultra-extreme walls (bubbles
of false vacuum decay) are discussed. Their respective energy densities are
higher and lower than that of the corresponding extreme (supersymmetric),
planar domain wall. These singularity free space-times exhibit non-trivial
causal structure analogous to certain non-extreme black holes. We focus on
anti-de~Sitter--Minkowski walls and comment on Minkowski--Minkowski walls with
trivial extreme limit, as well as walls adjacent to de~Sitter space-times with
no extreme limit.Comment: Revised version, 4 pages of REVTEX, UPR-546-T/Rev. Two figures not
included. This version contains further elaboration of the space-time causal
structur
Deformation Quantization of Geometric Quantum Mechanics
Second quantization of a classical nonrelativistic one-particle system as a
deformation quantization of the Schrodinger spinless field is considered. Under
the assumption that the phase space of the Schrodinger field is ,
both, the Weyl-Wigner-Moyal and Berezin deformation quantizations are discussed
and compared. Then the geometric quantum mechanics is also quantized using the
Berezin method under the assumption that the phase space is
endowed with the Fubini-Study Kahlerian metric. Finally, the Wigner function
for an arbitrary particle state and its evolution equation are obtained. As is
shown this new "second quantization" leads to essentially different results
than the former one. For instance, each state is an eigenstate of the total
number particle operator and the corresponding eigenvalue is always .Comment: 27+1 pages, harvmac file, no figure
Possible types of the evolution of vacuum shells around the de Sitter space
All possible evolution scenarios of a thin vacuum shell surrounding the
spherically symmetric de Sitter space have been determined and the
corresponding global geometries have been constructed. Such configurations can
appear at the final stage of the cosmological phase transition, when isolated
regions (islands) of the old vacuum remain. The islands of the old vacuum are
absorbed by the new vacuum, expand unlimitedly, or form black holes and
wormholes depending on the sizes of the islands as well as on the density and
velocity of the shells surrounding the islands.Comment: 3 pages, 1 figur
Singular shell embedded into a cosmological model
We generalize Israel's formalism to cover singular shells embedded in a
non-vacuum Universe. That is, we deduce the relativistic equation of motion for
a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker
spacetime. Also, we review the embedding of a Schwarzschild mass into a
cosmological model using "curvature" coordinates and give solutions with
(Sch/FLRW) and without the embedded mass (FLRW).Comment: 25 pages, 2 figure
Gravitation on a Homogeneous Domain
Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1}
a particular role is being played by conformal deformations. These are
conveniently described by using the homogeneous space for the conformal group
SU(2,2)/S(U(2)x U(2)) and its Shilov boundary - the compactified Minkowski
space \tilde{M} [1]. In this paper we review the geometrical structure involved
in such a description. In particular we demonstrate that coherent states on the
homogeneous Kae}hler domain give rise to Einstein-like plastic conformal
deformations when extended to \tilde{M} [2].Comment: 10 pages, 1 figure; four misprints in the original version corrected:
one lacking closing parenthesis, two letters, and an overall sign in front of
the primitive function on p.
Covariant perturbations of domain walls in curved spacetime
A manifestly covariant equation is derived to describe the perturbations in a
domain wall on a given background spacetime. This generalizes recent work on
domain walls in Minkowski space and introduces a framework for examining the
stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0
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