21 research outputs found
The basis of nonlocal curvature invariants in quantum gravity theory
A complete basis of nonlocal invariants in quantum gravity theory is built to
third order in spacetime curvature and matter-field strengths. The nonlocal
identities are obtained which reduce this basis for manifolds with
dimensionality . The present results are used in heat-kernel theory,
theory of gauge fields and serve as a basis for the model-independent approach
to quantum gravity and, in particular, for the study of nonlocal vacuum effects
in the gravitational collapse problem.Comment: 28 pages, REVTeX, Alberta Thy 14-9
Asymptotic behaviours of the heat kernel in covariant perturbation theory
The trace of the heat kernel is expanded in a basis of nonlocal curvature
invariants of th order. The coefficients of this expansion (the nonlocal
form factors) are calculated to third order in the curvature inclusive. The
early-time and late-time asymptotic behaviours of the trace of the heat kernel
are presented with this accuracy. The late-time behaviour gives the criterion
of analyticity of the effective action in quantum field theory. The latter
point is exemplified by deriving the effective action in two dimensions.Comment: 22 pages, REVTeX, Alberta Thy 45-9
Plane torsion waves in quadratic gravitational theories
The definition of the Riemann-Cartan space of the plane wave type is given.
The condition under which the torsion plane waves exist is found. It is
expressed in the form of the restriction imposed on the coupling constants of
the 10-parametric quadratic gravitational Lagrangian. In the mathematical
appendix the formula for commutator of the variation operator and Hodge
operator is proved. This formula is applied for the variational procedure when
the gravitational field equations are obtained in terms of the exterior
differential forms.Comment: 3 May 1998. - 11
Dyonic Wormholes in 5D Kaluza-Klein Theory
New spherically symmetric dyonic solutions, describing a wormhole-like class
of spacetime configurations in five-dimensional Kaluza-Klein theory, are given
in an explicit form. For this type of solution the electric and magnetic fields
cause a significantly different global structure. For the electric dominated
case, the solution is everywhere regular but, when the magnetic strength
overcomes the electric contribution, the mouths of the wormhole become singular
points. When the electric and magnetic charge parameters are identical, the
throats ``degenerate'' and the solution reduces to the trivial embedding of the
four-dimensional massless Reissner-Nordstr{\"o}m black hole solution. In
addition, their counterparts in eleven-dimensional supergravity are constructed
by a non-trivial uplifting.Comment: Revised version to appear in Class. Quant. Gra
Some Spinor-Curvature Identities
We describe a class of spinor-curvature identities which exist for Riemannian
or Riemann-Cartan geometries. Each identity relates an expression quadratic in
the covariant derivative of a spinor field with an expression linear in the
curvature plus an exact differential. Certain special cases in 3 and 4
dimensions which have been or could be used in applications to General
Relativity are noted.Comment: 5 pages Plain TeX, NCU-GR-93-SSC
Pleba\'nski-Demia\'nski-like solutions in metric-affine gravity
We consider a (non--Riemannian) metric--affine gravity theory, in particular
its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell
theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely
the Pleba\'nski--Demia\'nski class of Petrov type D metrics.Comment: 12 pages of a LaTeX-fil
Cosmological Landscape From Nothing: Some Like It Hot
We suggest a novel picture of the quantum Universe -- its creation is
described by the {\em density matrix} defined by the Euclidean path integral.
This yields an ensemble of universes -- a cosmological landscape -- in a mixed
state which is shown to be dynamically more preferable than the pure quantum
state of the Hartle-Hawking type. The latter is dynamically suppressed by the
infinitely large positive action of its instanton, generated by the conformal
anomaly of quantum fields within the cosmological bootstrap (the
self-consistent back reaction of hot matter). This bootstrap suggests a
solution to the problem of boundedness of the on-shell cosmological action and
eliminates the infrared catastrophe of small cosmological constant in Euclidean
quantum gravity. The cosmological landscape turns out to be limited to a
bounded range of the cosmological constant . The domain is ruled out by the
back reaction effect which we analyze by solving effective Euclidean equations
of motion. The upper cutoff is enforced by the quantum effects of vacuum energy
and the conformal anomaly mediated by a special ghost-avoidance renormalization
of the effective action. They establish a new quantum scale
which is determined by the coefficient of the topological Gauss-Bonnet term in
the conformal anomaly. This scale is realized as the upper bound -- the
limiting point of an infinite sequence of garland-type instantons which
constitute the full cosmological landscape. The dependence of the cosmological
constant range on particle phenomenology suggests a possible dynamical
selection mechanism for the landscape of string vacua.Comment: Final version, to appear in JCA
Can Galactic Observations Be Explained by a Relativistic Gravity Theory?
We consider the possibility of an alternative gravity theory explaining the
dynamics of galactic systems without dark matter. From very general assumptions
about the structure of a relativistic gravity theory we derive a general
expression for the metric to order . This allows us to compare the
predictions of the theory with various experimental data: the Newtonian limit,
light deflection and retardation, rotation of galaxies and gravitational
lensing. Our general conclusion is that the possibility for any gravity theory
to explain the behaviour of galaxies without dark matter is rather improbable.Comment: 12p, REVTeX 3.