61 research outputs found
Back Reaction and Semiclassical Approximation of cosmological models coupled to matter
Bianchi -I, -III, and FRW type models minimally coupled to a massive
spatially homogeneous scalar field (i.e. a particle) are studied in the
framework of semiclassical quantum gravity. In a first step we discuss the
solutions of the corresponding equation for a Schr\"odinger particle
propagating on a classical background. The back reaction of the Schr\"odinger
particle on the classical metric is calculated by means of the Wigner function
and by means of the expectation value of the energy-momentum-tensor of the
field as a source. Both methods in general lead to different results.Comment: 4 pages, Latex, to appear in: Proceedings of the Second Meeting on
constrained Dynamics and Quantum Gravity (Santa Margherita Ligure 1996
On the Quantum Levels of Isolated Spherically Symmetric Gravitational Systems
The known canonical quantum theory of a spherically symmetric pure
(Schwarzschild) gravitational system describes isolated black holes by plane
waves exp(-iMc^2\tau/\hbar) with respect to their continuous masses M and the
proper time \tau of obsevers at spatial infinity. On the other hand Bekenstein
and Mukhanov postulated discrete mass levels for such black holes in the spirit
of the Bohr-Sommerfeld quantisation in atomic physics. The two approaches can
be related by postulating periodic boundary conditions in time for the plane
waves and by identifying the period \Delta in real time with the period
\Delta_H= 8\pi GM/c^3 in Euclidean time. This yields the mass spectrum
M_n=(1/2)\sqrt{n}m_P, n=1,2,... .Comment: 13 pages, LaTeX, Replacement corrects a few misprints. No change of
content
Remarks on the Configuration Space Approach to Spin-Statistics
The angular momentum operators for a system of two spin-zero
indistinguishable particles are constructed, using Isham's Canonical Group
Quantization method. This mathematically rigorous method provides a hint at the
correct definition of (total) angular momentum operators, for arbitrary spin,
in a system of indistinguishable particles. The connection with other
configuration space approaches to spin-statistics is discussed, as well as the
relevance of the obtained results in view of a possible alternative proof of
the spin-statistics theorem.Comment: 18 page
Existence of a Semiclassical Approximation in Loop Quantum Gravity
We consider a spherical symmetric black hole in the Schwarzschild metric and
apply Bohr-Sommerfeld quantization to determine the energy levels. The
canonical partition function is then computed and we show that the entropy
coincides with the Bekenstein-Hawking formula when the maximal number of states
for the black hole is the same as computed in loop quantum gravity, proving in
this case the existence of a semiclassical limit and obtaining an independent
derivation of the Barbero-Immirzi parameter.Comment: 6 pages, no figures. Final version accepted for publication in
General Relativity and Gravitatio
Postmodern String Theory: Stochastic Formulation
In this paper we study the dynamics of a statistical ensemble of strings,
building on a recently proposed gauge theory of the string geodesic field. We
show that this stochastic approach is equivalent to the Carath\'eodory
formulation of the Nambu-Goto action, supplemented by an averaging procedure
over the family of classical string world-sheets which are solutions of the
equation of motion. In this new framework, the string geodesic field is
reinterpreted as the Gibbs current density associated with the string
statistical ensemble. Next, we show that the classical field equations derived
from the string gauge action, can be obtained as the semi-classical limit of
the string functional wave equation. For closed strings, the wave equation
itself is completely analogous to the Wheeler-DeWitt equation used in quantum
cosmology. Thus, in the string case, the wave function has support on the space
of all possible spatial loop configurations. Finally, we show that the string
distribution induces a multi-phase, or {\it cellular} structure on the
spacetime manifold characterized by domains with a purely Riemannian geometry
separated by domain walls over which there exists a predominantly Weyl
geometry.Comment: 24pages, ReVTe
Spherically Symmetric Gravity as a Completely Integrable System
It is shown - in Ashtekar's canonical framework of General Relativity - that
spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time
constitutes a finite dimensional completely integrable system. Canonically
conjugate observables for asymptotically flat space-times are masses as action
variables and - surprisingly - time variables as angle variables, each of which
is associated with an asymptotic "end" of the Cauchy surfaces. The emergence of
the time observable is a consequence of the Hamiltonian formulation and its
subtleties concerning the slicing of space and time and is not in contradiction
to Birkhoff's theorem. The results are of interest as to the concept of time in
General Relativity. They can be formulated within the ADM formalism, too.
Quantization of the system and the associated Schr\"odinger equation depend on
the allowed spectrum of the masses.Comment: 20.p., Latex, PITHA 93-3
Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
We show that the quantization of spherically symmetric pure gravity can be
carried out completely in the framework of Ashtekar's self-dual representation.
Consistent operator orderings can be given for the constraint functionals
yielding two kinds of solutions for the constraint equations, corresponding
classically to globally nondegenerate or degenerate metrics. The physical state
functionals can be determined by quadratures and the reduced Hamiltonian system
possesses 2 degrees of freedom, one of them corresponding to the classical
Schwarzschild mass squared and the canonically conjugate one representing a
measure for the deviation of the nonstatic field configurations from the static
Schwarzschild one. There is a natural choice for the scalar product making the
2 fundamental observables self-adjoint. Finally, a unitary transformation is
performed in order to calculate the triad-representation of the physical state
functionals and to provide for a solution of the appropriately regularized
Wheeler-DeWitt equation.Comment: 43 page
Spacetime Foam Model of the Schwarzschild Horizon
We consider a spacetime foam model of the Schwarzschild horizon, where the
horizon consists of Planck size black holes. According to our model the entropy
of the Schwarzschild black hole is proportional to the area of its event
horizon. It is possible to express geometrical arguments to the effect that the
constant of proportionality is, in natural units, equal to one quarter.Comment: 16 pages, 2 figures, improved and extended version with some
significant changes. Accepted for publication in Phys.Rev.
Quantum Black Holes from Quantum Collapse
The Schwarzschild black hole can be viewed as the special case of the
marginally bound Lema\^\i tre-Tolman-Bondi models of dust collapse which
corresponds to a constant mass function. We have presented a midi-superspace
quantization of this model for an arbitrary mass-function in a separate
publication. In this communication we show that our solution leads both to
Bekenstein's area spectrum for black holes as well as to the black hole
entropy, which, in this context, is naturally interpreted as the loss of
information of the original matter distribution within the collapsing dust
cloud.Comment: LaTeX file, 6 pages, 1 figure, Paper re-written into sections, some
references added, some elaborations, conclusions unchanged, to appear in
Physical Review
Area spectrum and quasinormal modes of black holes
We demonstrate that an equidistant area spectrum for the link variables in
loop quantum gravity can reproduce both the thermodynamics and the quasinormal
mode properties of black holes.Comment: 11 pages, no figures; references adde
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