544 research outputs found
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Dirac Quantization of Two-Dimensional Dilaton Gravity Minimally Coupled to N Massless Scalar Fields
It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylinder
can be consistently quantized (using Dirac's approach) without imposing any
constraints on the sign of the gravitational coupling constant or the sign (or
value) of the cosmological constant. The quantum constraints in terms of the
original geometrical variables are also derived
Consistency of Semiclassical Gravity
We discuss some subtleties which arise in the semiclassical approximation to
quantum gravity. We show that integrability conditions prevent the existence of
Tomonaga-Schwinger time functions on the space of three-metrics but admit them
on superspace. The concept of semiclassical time is carefully examined. We
point out that central charges in the matter sector spoil the consistency of
the semiclassical approximation unless the full quantum theory of gravity and
matter is anomaly-free. We finally discuss consequences of these considerations
for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2
Free fields via canonical transformations of matter-coupled 2D dilaton gravity models
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation
We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression
for the finite residual gauge transformations has been worked ou
Mass Superselection, Canonical Gauge Transformations, and Asymptotically Flat Variational Principles
The phase space reduction of Schwarzschild black holes by Thiemann and
Kastrup and by Kucha\v{r} is reexamined from a different perspective on gauge
freedom. This perspective introduces additional gauge transformations which
correspond to asymptotically nontrivial diffeomorphisms. Various subtleties
concerning variational principles for asymptotically flat systems are addressed
which allow us to avoid the usual conclusion that treating such transformations
as gauge implies the vanishing of corresponding total charges. Instead,
superselection rules are found for the (nonvanishing) ADM mass at the
asymptotic boundaries. The addition of phenomenological clocks at each
asymptotic boundary is also studied and compared with the `parametrization
clocks' of Kucha\v{r}.Comment: 15 pages, ReVTeX, Minor changes made in response to referee's
commment
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
Towards the graviton from spinfoams: the 3d toy model
Recently, a proposal has appeared for the extraction of the 2-point function
of linearised quantum gravity, within the spinfoam formalism. This relies on
the use of a boundary state, which introduces a semi-classical flat geometry on
the boundary. In this paper, we investigate this proposal considering a toy
model in the (Riemannian) 3d case, where the semi-classical limit is better
understood. We show that in this limit the propagation kernel of the model is
the one for the harmonic oscillator. This is at the origin of the expected 1/L
behaviour of the 2-point function. Furthermore, we numerically study the short
scales regime, where deviations from this behaviour occur.Comment: 8 pages, 2 figures; v3 revised versio
A Probability-Base Alerting Logic for Aircraft on Parallel Approach
This document discusses the development and evaluation of an airborne collision alerting logic for aircraft on closely-spaced approaches to parallel runways. A novel methodology is used when links alerts to collision probabilities: alerting thresholds are set such that when the probability of a collision exceeds an acceptable hazard level an alert is issued. The logic was designed to limit the hazard level to that estimated for the Precision Runway Monitoring system: one accident in every one thousand blunders which trigger alerts. When the aircraft were constrained to be coaltitude, evaluations of a two-dimensional version of the alerting logic show that the achieved hazard level is approximately one accident in every 250 blunders. Problematic scenarios have been identified and corrections to the logic can be made. The evaluations also show that over eighty percent of all unnecessary alerts were issued during scenarios in which the miss distance would have been less than 1000 ft, indicating that the alerts may have been justified. Also, no unnecessary alerts were generated during normal approaches
Quantum creation of an Inhomogeneous universe
In this paper we study a class of inhomogeneous cosmological models which is
a modified version of what is usually called the Lema\^itre-Tolman model. We
assume that we have a space with 2-dimensional locally homogeneous spacelike
surfaces. In addition we assume they are compact. Classically we investigate
both homogeneous and inhomogeneous spacetimes which this model describe. For
instance one is a quotient of the AdS space which resembles the BTZ black
hole in AdS.
Due to the complexity of the model we indicate a simpler model which can be
quantized easily. This model still has the feature that it is in general
inhomogeneous. How this model could describe a spontaneous creation of a
universe through a tunneling event is emphasized.Comment: 21 pages, 5 ps figures, REVTeX, new subsection include
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