1,730 research outputs found
A theory of thin shells with orbiting constituents
The self-gravitating, spherically symmetric thin shells built of orbiting
particles are sstudied. Two new features are found. One is the minimal possible
value for an angular momentum of particles, above which elleptic orbits become
possible. The second is the coexistence of both the wormhole solutions and the
elleptic or hyperbolic orbits for the same values of the parameters (but
different initial conditions). Possible applications of these results to
astrophysics and quantum black holes are briefly discussed.Comment: 22 pages, Latex, 10 eps figures. CERN preprint no. CERN-TH 2000-16
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
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
Quantum geometrodynamics for black holes and wormholes
The geometrodynamics of the spherical gravity with a selfgravitating thin
dust shell as a source is constructed. The shell Hamiltonian constraint is
derived and the corresponding Schroedinger equation is obtained. This equation
appeared to be a finite differences equation. Its solutions are required to be
analytic functions on the relevant Riemannian surface. The method of finding
discrete spectra is suggested based on the analytic properties of the
solutions. The large black hole approximation is considered and the discrete
spectra for bound states of quantum black holes and wormholes are found. They
depend on two quantum numbers and are, in fact, quasicontinuous.Comment: Latex, 32 pages, 5 fig
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
Symplectic geometries on supermanifolds
Extension of symplectic geometry on manifolds to the supersymmetric case is
considered. In the even case it leads to the even symplectic geometry (or,
equivalently, to the geometry on supermanifolds endowed with a non-degenerate
Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is
proven that in the odd case there are two different scalar symplectic
structures (namely, an odd closed differential 2-form and the antibracket)
which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten
Vacuum decay via Lorentzian wormholes
We speculate about the spacetime description due to the presence of
Lorentzian wormholes (handles in spacetime joining two distant regions or other
universes) in quantum gravity. The semiclassical rate of production of these
Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a
result of the spontaneous decay of vacuum due to a real tunneling
configuration. In the magnetic case it only depends on the field theoretical
fine structure constant. We predict that the quantum probability corresponding
to the nucleation of such geodesically complete spacetimes should be actually
negligible in our physical Universe
Canonical and D-transformations in Theories with Constraints
A class class of transformations in a super phase space (we call them
D-transformations) is described, which play in theories with second-class
constraints the role of ordinary canonical transformations in theories without
constraints.Comment: 16 pages, LaTe
Degree of entanglement as a physically ill-posed problem: The case of entanglement with vacuum
We analyze an example of a photon in superposition of different modes, and
ask what is the degree of their entanglement with vacuum. The problem turns out
to be ill-posed since we do not know which representation of the algebra of
canonical commutation relations (CCR) to choose for field quantization. Once we
make a choice, we can solve the question of entanglement unambiguously. So the
difficulty is not with mathematics, but with physics of the problem. In order
to make the discussion explicit we analyze from this perspective a popular
argument based on a photon leaving a beam splitter and interacting with two
two-level atoms. We first solve the problem algebraically in Heisenberg
picture, without any assumption about the form of representation of CCR. Then
we take the -representation and show in two ways that in two-mode
states the modes are maximally entangled with vacuum, but single-mode states
are not entangled. Next we repeat the analysis in terms of the representation
of CCR taken from Berezin's book and show that two-mode states do not involve
the mode-vacuum entanglement. Finally, we switch to a family of reducible
representations of CCR recently investigated in the context of field
quantization, and show that the entanglement with vacuum is present even for
single-mode states. Still, the degree of entanglement is here difficult to
estimate, mainly because there are subsystems, with unspecified and
large.Comment: This paper is basically a reply to quant-ph/0507189 by S. J. van Enk
and to the remarks we got from L. Vaidman after our preliminary
quant-ph/0507151. Version accepted in Phys. Rev.
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