14 research outputs found
The quasi-classical model of the spherical configuration in general relativity
We consider the quasi-classical model of the spin-free configuration on the
basis of the self-gravitating spherical dust shell in General Relativity. For
determination of the energy spectrum of the stationary states on the basis of
quasi-classical quantization rules it is required to carry out some
regularization of the system. It is realized by an embedding of the initial
system in the extended system with rotation. Then, the stationary states of the
spherical shells are S-states of the system with the intrinsic momentum. The
quasi-classical treatment of a stability of the configuration is associated
with the Langer modification of a square of the quantum mechanical intrinsic
momentum. It gives value of critical bare mass of the shell determining
threshold of stability. For the shell with the bare mass smaller or equal to
the Planck's mass, the energy spectra of bound states are found. We obtain the
expression for tunneling probability of the shell and construct the
quasi-classical model of the pair creation and annihilation of the shells.Comment: 22 pages, sprocl.sty, 3 figure
On the variational principle for dust shells in General Relativity
The variational principle for a thin dust shell in General Relativity is
constructed. The principle is compatible with the boundary-value problem of the
corresponding Euler-Lagrange equations, and leads to ``natural boundary
conditions'' on the shell. These conditions and the gravitational field
equations which follow from an initial variational principle, are used for
elimination of the gravitational degrees of freedom. The transformation of the
variational formula for spherically-symmetric systems leads to two natural
variants of the effective action. One of these variants describes the shell
from a stationary interior observer's point of view, another from the exterior
one. The conditions of isometry of the exterior and interior faces of the shell
lead to the momentum and Hamiltonian constraints. The canonical equivalence of
the mentioned systems is shown in the extended phase space. Some particular
cases are considered.Comment: 25 pages, RevTeX, no figures, revised version, typos corrected,
accepted for publication in Journal of Mathematical Physic
Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in General Relativity
We propose the method of investigation of radial motions for charged and
neutral test particles in the Reissner-Nordstr\"{o}m field by means of mass
potential. In this context we analyze special features of interaction of
charges and their motions in General Relativity and construct the radial motion
classification. For test particles and a central source with charges and
, respectively, the conditions of attraction (when ) and repulsion
(when ) are obtained. The conditions of motionless test particle states
with respect to the central source are investigated and, in addition, stability
conditions for such static equilibrium states are found. It is shown that
stable states are possible only for the bound states of weakly charged
particles in the field of a naked singularity. Frequencies of small
oscillations of test particles near their equilibrium positions are also found.Comment: 15 pages, 9 figure