71 research outputs found
Mode decomposition and unitarity in quantum cosmology, Talk given at the Second Meeting on Constrained Dynamics and Quantum gravity, Santa Margherita Ligure, September 17-21, 1996
Contrary to common belief, there are perspectives for generalizing the notion
of positive and negative frequency in minisuperspace quantum cosmology, even
when the wave equation does not admit symmetries. We outline a strategy in
doing so when the potential is positive. Also, an underlying unitarity
structure shows up. Starting in the framework of the Klein-Gordon type
quantization, I am led to a result that relies on global features on the model,
and that is possibly related to structures encountered in the refined algebraic
quantization scheme.Comment: 5 pages, LaTeX (no figures
Complex lapse, complex action and path integrals
Imaginary time is often used in quantum tunnelling calculations. This article
advocates a conceptually sounder alternative: complex lapse. In the ``3+1''
action for the Einstein gravitational field minimally coupled to a Klein-Gordon
field, allowing the lapse function to be complex yields a complex action which
generates both the usual Lorentzian theory and its Riemannian analogue, and in
particular allows a change of signature between the two. The action and
variational equations are manifestly well defined in the Hamiltonian
representation, with the momentum fields consequently being complex. The
complex action interpolates between the Lorentzian and Riemannian actions as
they appear formally in the respective path integrals. Thus the complex-lapse
theory provides a unified basis for a path-integral quantum theory of gravity
involving both Lorentzian and Riemannian aspects. A major motivation is the
quantum-tunnelling scenario for the origin of the universe. Taken as an
explanation for the observed quantum tunnelling of particles, the complex-lapse
theory determines that the argument of the lapse for the universe now is
extremely small but negative.Comment: 12 pages, Te
The trace left by signature-change-induced compactification
Recently, it has been shown that an infinite succession of classical
signature changes (''signature oscillations'') can compactify and stabilize
internal dimensions, and simultaneously leads, after a coarse graining type of
average procedure, to an effective (''physical'') space-time geometry
displaying the usual Lorentzian metric signature. Here, we consider a minimally
coupled scalar field on such an oscillating background and study its effective
dynamics. It turns out that the resulting field equation in four dimensions
contains a coupling to some non-metric structure, the imprint of the
''microscopic'' signature oscillations on the effective properties of matter.
In a multidimensional FRW model, this structure is identical to a massive
scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure
Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'
Kossowski and Kriele derived boundary conditions on the metric at a surface
of signature change. We point out that their derivation is based not only on
certain smoothness assumptions but also on a postulated form of the Einstein
field equations. Since there is no canonical form of the field equations at a
change of signature, their conclusions are not inescapable. We show here that a
weaker formulation is possible, in which less restrictive smoothness
assumptions are made, and (a slightly different form of) the Einstein field
equations are satisfied. In particular, in this formulation it is possible to
have a bounded energy-momentum tensor at a change of signature without
satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum
Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996
Actions for signature change
This is a contribution on the controversy about junction conditions for
classical signature change. The central issue in this debate is whether the
extrinsic curvature on slices near the hypersurface of signature change has to
be continuous ({\it weak} signature change) or to vanish ({\it strong}
signature change). Led by a Lagrangian point of view, we write down eight
candidate action functionals ,\dots as possible generalizations of
general relativity and investigate to what extent each of these defines a
sensible variational problem, and which junction condition is implied. Four of
the actions involve an integration over the total manifold. A particular
subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian
density . The other four actions are constructed as sums of
integrals over singe-signature domains. The result is that {\it both} types of
junction conditions occur in different models, i.e. are based on different
first principles, none of which can be claimed to represent the ''correct''
one, unless physical predictions are taken into account. From a point of view
of naturality dictated by the variational formalism, {\it weak} signature
change is slightly favoured over {\it strong} one, because it requires less
{\it \`a priori} restrictions for the class of off-shell metrics. In addition,
a proposal for the use of the Lagrangian framework in cosmology is made.Comment: 36 pages, LaTeX, no figures; some corrections have been made, several
Comments and further references are included and a note has been added
Gravity and Signature Change
The use of proper ``time'' to describe classical ``spacetimes'' which contain
both Euclidean and Lorentzian regions permits the introduction of smooth
(generalized) orthonormal frames. This remarkable fact permits one to describe
both a variational treatment of Einstein's equations and distribution theory
using straightforward generalizations of the standard treatments for constant
signature.Comment: Plain TeX, 6 pages; to appear in GR
BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE
We show that, contrary to recent criticism, our previous work yields a
reasonable class of solutions for the massless scalar field in the presence of
signature change.Comment: 11 pages, Plain Tex, no figure
Closed Strings with Low Harmonics and Kinks
Low-harmonic formulas for closed relativistic strings are given. General
parametrizations are presented for the addition of second- and third-harmonic
waves to the fundamental wave. The method of determination of the
parametrizations is based upon a product representation found for the finite
Fourier series of string motion in which the constraints are automatically
satisfied. The construction of strings with kinks is discussed, including
examples. A procedure is laid out for the representation of kinks that arise
from self-intersection, and subsequent intercommutation, for harmonically
parametrized cosmic strings.Comment: 39, CWRUTH-93-
Evolution of cosmic string configurations
We extend and develop our previous work on the evolution of a network of
cosmic strings. The new treatment is based on an analysis of the probability
distribution of the end-to-end distance of a randomly chosen segment of
left-moving string of given length. The description involves three distinct
length scales: , related to the overall string density, , the
persistence length along the string, and , describing the small-scale
structure, which is an important feature of the numerical simulations that have
been done of this problem. An evolution equation is derived describing how the
distribution develops in time due to the combined effects of the universal
expansion, of intercommuting and loop formation, and of gravitational
radiation. With plausible assumptions about the unknown parameters in the
model, we confirm the conclusions of our previous study, that if gravitational
radiation and small-scale structure effects are neglected, the two dominant
length scales both scale in proportion to the horizon size. When the extra
effects are included, we find that while and grow,
initially does not. Eventually, however, it does appear to scale, at a much
lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4,
IMPERIAL/TP/92-93/4
Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes
We study the phenomenon of gyroscopic precession and the analogues of
inertial forces within the framework of general relativity. Covariant
connections between the two are established for circular orbits in stationary
spacetimes with axial symmetry. Specializing to static spacetimes, we prove
that gyroscopic precession and centrifugal force both reverse at the photon
orbits. Simultaneous non-reversal of these in the case of stationary spacetimes
is discussed. Further insight is gained in the case of static spacetime by
considering the phenomena in a spacetime conformal to the original one.
Gravi-electric and gravi-magnetic fields are studied and their relation to
inertial forces is established.Comment: 21 pages, latex, no figures, http://202.41.67.76/~nayak/gpifass.te
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