167 research outputs found
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
Coherent States of groups
This work can be considered as a continuation of our previous one (J.Phys.,
26 (1993) 313), in which an explicit form of coherent states (CS) for all SU(N)
groups was constructed by means of representations on polynomials. Here we
extend that approach to any SU(l,1) group and construct explicitly
corresponding CS. The CS are parametrized by dots of a coset space, which is,
in that particular case, the open complex ball . This space together
with the projective space , which parametrizes CS of the SU(l+1) group,
exhausts all complex spaces of constant curvature. Thus, both sets of CS
provide a possibility for an explicit analysis of the quantization problem on
all the spaces of constant curvature.Comment: 22 pages, to be published in "Journal of Physics A
Vacuum shell in the Schwarzschild-de Sitter world
We construct the classification scheme for all possible evolution scenarios
and find the corresponding global geometries for dynamics of a thin spherical
vacuum shell in the Schwarzschild-de Sitter metric. This configuration is
suitable for the modelling of vacuum bubbles arising during cosmological phase
transitions in the early Universe. The distinctive final types of evolution
from the local point of view of a rather distant observer are either the
unlimited expansion of the shell or its contraction with a formation of black
hole (with a central singularity) or wormhole (with a baby universe in
interior).Comment: 15 pages, 8 figure
Evolution of a vacuum shell in the Friedman-Schwarzschild world
The method of an effective potential is used to investigate the possible
types of evolution of vacuum shells in the Friedman-Schwarzschild world. Such
shells are assumed to emerge during phase transitions in the early Universe.
The possible global geometries are constructed for the Friedman- Schwarzschild
worlds. Approximate solutions to the equation of motion of a vacuum shell have
been found. The conditions under which the end result of the evolution of the
vacuum shells under consideration is the formation of black holes and wormholes
with baby universes inside have been found. The interior of this world can be a
closed, flat, or open Friedman universe.Comment: 12 pages, 4 figure
Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity
It is shown that in non-linear electrodynamics (in particular, Born-Infeld
one) in the framework of general relativity there exist "weakly singular"
configurations such that (i) the proper mass M is finite in spite of
divergences of the energy density, (ii) the electric charge q and Schwarzschild
mass m ~ q can be made as small as one likes, (iv) all field and energy
distributions are concentrated in the core region. This region has an almost
zero surface area but a finite longitudinal size L=2M. Such configurations can
be viewed as a new version of a classical analogue of an elementary particle.Comment: 11 pages. 1 reference added. To appear in Grav. Cosm
Open Superstring Star as a Continuous Moyal Product
By diagonalizing the three-string vertex and using a special coordinate
representation the matter part of the open superstring star is identified with
the continuous Moyal product of functions of anti-commuting variables. We show
that in this representation the identity and sliver have simple expressions.
The relation with the half-string fermionic variables in continuous basis is
given.Comment: Latex, 19 pages; more comments added and notations are simplifie
Analytic representations based on SU(1,1) coherent states and their applications
We consider two analytic representations of the SU(1,1) Lie group: the
representation in the unit disk based on the SU(1,1) Perelomov coherent states
and the Barut-Girardello representation based on the eigenstates of the SU(1,1)
lowering generator. We show that these representations are related through a
Laplace transform. A ``weak'' resolution of the identity in terms of the
Perelomov SU(1,1) coherent states is presented which is valid even when the
Bargmann index is smaller than one half. Various applications of these
results in the context of the two-photon realization of SU(1,1) in quantum
optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More
information on http://www.technion.ac.il/~brif/science.htm
Stable branches of a solution for a fermion on domain wall
We discuss the case when a fermion occupies an excited non-zero frequency
level in the field of domain wall. We demonstrate that a solution exists for
the coupling constant in the limited interval . We
show that indeed there are different branches of stable solution for in
this interval. The first one corresponds to a fermion located on the domain
wall (). The second branch, which belongs to the interval
, describes a polarized fermion off the domain
wall. The third branch with describes an excited antifermion in
the field of the domain wall.Comment: 15 pages, 7 figures, references adde
Minkowski superspaces and superstrings as almost real-complex supermanifolds
In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that
mathematicians study are real or (almost) complex ones, while Minkowski
superspaces are completely different objects. They are what we call almost
real-complex supermanifolds, i.e., real supermanifolds with a non-integrable
distribution, the collection of subspaces of the tangent space, and in every
subspace a complex structure is given.
An almost complex structure on a real supermanifold can be given by an even
or odd operator; it is complex (without "always") if the suitable superization
of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we
define the circumcised analog of the Nijenhuis tensor. We compute it for the
Minkowski superspaces and superstrings. The space of values of the circumcised
Nijenhuis tensor splits into (indecomposable, generally) components whose
irreducible constituents are similar to those of Riemann or Penrose tensors.
The Nijenhuis tensor vanishes identically only on superstrings of
superdimension 1|1 and, besides, the superstring is endowed with a contact
structure. We also prove that all real forms of complex Grassmann algebras are
isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to
related recent work by Witten is adde
Mass Quantization of the Schwarzschild Black Hole
We examine the Wheeler-DeWitt equaton for a static, eternal Schwarzschild
black hole in Kucha\v r-Brown variables and obtain its energy eigenstates.
Consistent solutions vanish in the exterior of the Kruskal manifold and are
non-vanishing only in the interior. The system is reminiscent of a particle in
a box. States of definite parity avoid the singular geometry by vanishing at
the origin. These definite parity states admit a discrete energy spectrum,
depending on one quantum number which determines the Arnowitt-Deser-Misner
(ADM) mass of the black hole according to a relation conjectured long ago by
Bekenstein, . If attention is restricted only to these
quantized energy states, a black hole is described not only by its mass but
also by its parity. States of indefinite parity do not admit a quantized mass
spectrum.Comment: Change in eq. (13). Factors of 4 cleaned up. Refs. adde
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