76 research outputs found
Black hole mass spectrum vs spectrum of Hawking radiation
We consider a massive selfgravitating shell as a model for collapsing body
and a null selfgravitating shell as a model for quanta of Hawking radiation. It
is show that the mass-energy spectra for the body and the radiation do not
match. The way out of this difficulty is to consider not only out-going
radiation but also the ingoing one. It means that the structure of black hole
is changing during its evaporation resulting in the Bekenstein-Mukhanov
spectrum for large masses.Comment: 11 pages, 2 figures, submitted to Phys.Rev.Let
Junction Conditions of Friedmann-Robertson-Walker Space-Times
We complete a classification of junctions of two Friedmann-Robertson-Walker
space-times bounded by a spherical thin wall. Our analysis covers super-horizon
bubbles and thus complements the previous work of Berezin, Kuzumin and Tkachev.
Contrary to sub-horizon bubbles, various topology types for super-horizon
bubbles are possible, regardless of the sign of the extrinsic curvature. We
also derive a formula for the peculiar velocity of a domain wall for all types
of junction.Comment: 7 pages, LaTeX, figures are not included (available on request by
regular mail), WU-AP/31/9
Quasiclassical mass spectrum of the black hole model with selfgravitating dust shell
We consider a quantum mechanical black hole model introduced in {\it
Phys.Rev.}, {\bf D57}, 1118 (1998) that consists of the selfgravitating dust
shell. The Schroedinger equation for this model is a finite difference equation
with the shift of the argument along the imaginary axis. Solving this equation
in quasiclassical limit in complex domain leads to quantization conditions that
define discrete quasiclassical mass spectrum. One of the quantization
conditions is Bohr-Sommerfeld condition for the bound motion of the shell. The
other comes from the requirement that the wave function is unambiguously
defined on the Riemannian surface on which the coefficients of Schroedinger
equation are regular. The second quantization condition remains valid for the
unbound motion of the shell as well, and in the case of a collapsing null-dust
shell leads to spectrum.Comment: 35 pages, 8 figures, to appear in Phys. Rev.
Quantum Formation of Black Hole and Wormhole in Gravitational Collapse of a Dust Shell
Quantum-mechanical model of self-gravitating dust shell is considered. To
clarify the relation between classical and quantum spacetime which the shell
collapse form, we consider various time slicing on which quantum mechanics is
developed. By considering the static time slicing which corresponds to an
observer at a constant circumference radius, we obtain the wave functions of
the shell motion and the discrete mass spectra which specify the global
structures of spherically symmetric spacetime formed by the shell collapse. It
is found that wormhole states are forbidden when the rest mass is comparable
with Plank mass scale due to the zero-point quantum fluctuations.Comment: 10 pages in twocolumn, 8 figures, RevTeX 3.
Could the real (not virtual) static observer exist outside a Schwarzschild black hole?
The aim of this Letter is rather pedagogical. We considered the static
spherically symmetric ensemble of observers, having finite bare mass and trying
to measure geometrical and physical properties of the environmental static
(Schwarzschild) space-time. It is shown that, using the photon rockets (which
the mass together with the mass of their fuel is also taken into account) they
can managed to keep themselves on the fixed value of radius. The process of
diminishing the total bare mass up to zero lasts infinitely long time. It is
important that the problem is solved self-consistently, i.e., with full account
for the back reaction of both bare mass and radiation from rockets on the
space-time geometry.Comment: 7 page
Supersymmetry and the Odd Poisson Bracket
Some applications of the odd Poisson bracket developed by Kharkov's theorists
are represented, including the reformulation of classical Hamiltonian dynamics,
the description of hydrodynamics as a Hamilton system by means of the odd
bracket and the dynamics formulation with the Grassmann-odd Lagrangian. Quantum
representations of the odd bracket are also constructed and applied for the
quantization of classical systems based on the odd bracket and for the
realization of the idea of a composite spinor structure of space-time. At last,
the linear odd bracket, corresponding to a semi-simple Lie group, is introduced
on the Grassmann algebra.Comment: 17 pages, LATEX 2e. Invited talk given at the International Symposium
"30 Years of Supersymmetry" (Theoretical Physics Institute, University of
Minnesota, Minneapolis, MN, USA, 13-27 October, 2000) due to the support
kindly offered by the Organizing Committee of this meeting and, especially,
by Keith Olive and Mikhail Shifma
Boundary sources in the Doran - Lobo - Crawford spacetime
We take a null hypersurface (the causal horizon) generated by a congruence of
null geodesics as the boundary of the Doran-Lobo-Crawford spacetime, to be the
place where the Brown-York quasilocal energy is located. The components of the
outer and inner stress tensors are computed and shown to depend on time and on
the impact parameter of the test particle trajectory. The surface energy
density on the boundary is given by the same expression as that
obtained previously for the energy stored on a Rindler horizon.Comment: 4 pages, title changed, no figures, minor text change
Wick type deformation quantization of Fedosov manifolds
A coordinate-free definition for Wick-type symbols is given for symplectic
manifolds by means of the Fedosov procedure. The main ingredient of this
approach is a bilinear symmetric form defined on the complexified tangent
bundle of the symplectic manifold and subject to some set of algebraic and
differential conditions. It is precisely the structure which describes a
deviation of the Wick-type star-product from the Weyl one in the first order in
the deformation parameter. The geometry of the symplectic manifolds equipped by
such a bilinear form is explored and a certain analogue of the
Newlander-Nirenberg theorem is presented. The 2-form is explicitly identified
which cohomological class coincides with the Fedosov class of the Wick-type
star-product. For the particular case of K\"ahler manifold this class is shown
to be proportional to the Chern class of a complex manifold. We also show that
the symbol construction admits canonical superextension, which can be thought
of as the Wick-type deformation of the exterior algebra of differential forms
on the base (even) manifold. Possible applications of the deformed superalgebra
to the noncommutative field theory and strings are discussed.Comment: 20 pages, no figure
Ultimate gravitational mass defect
We present a new type of gravitational mass defect in which an infinite
amount of matter may be bounded in a zero ADM mass. This interpolates between
effects typical of closed worlds and T-spheres. We consider the Tolman model of
dust distribution and show that this phenomenon reveals itself for a solution
that has no origin on one side but is closed on the other side. The second
class of examples corresponds to smooth gluing T-spheres to the portion of the
Friedmann-Robertson-Walker solution. The procedure is generalized to
combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In
particular, in this approach a finite T-sphere is obtained that looks for
observers in two R-regions as the Schwarzschild metric with two different
masses one of which may vanish.Comment: 9 pages. 1 reference added. To appear in Gen. Rel. Gra
Hawking Radiation as Quantum Tunneling in Rindler Coordinate
We substantiate the Hawking radiation as quantum tunneling of fields or
particles crossing the horizon by using the Rindler coordinate. The thermal
spectrum detected by an accelerated particle is interpreted as quantum
tunneling in the Rindler spacetime. Representing the spacetime near the horizon
locally as a Rindler spacetime, we find the emission rate by tunneling, which
is expressed as a contour integral and gives the correct Boltzmann factor. We
apply the method to non-extremal black holes such as a Schwarzschild black
hole, a non-extremal Reissner-Nordstr\"{o}m black hole, a charged Kerr black
hole, de Sitter space, and a Schwarzschild-anti de Sitter black hole.Comment: LaTex 19 pages, no figure; references added and replaced by the
version accepted in JHE
- …