29 research outputs found
Scaling Solutions and reconstruction of Scalar Field Potentials
Starting from the hypothesis of scaling solutions, the general exact form of
the scalar field potential is found. In the case of two fluids, it turns out to
be a negative power of hyperbolic sine. In the case of three fluids the
analytic form is not found, but is obtained by quadratures.Comment: 5 pages, 2 figures, some changes in references and figures caption
Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics
A framework is introduced which explains the existence and similarities of
most exact solutions of the Einstein equations with a wide range of sources for
the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian
formulation. This class includes the spatially homogeneous cosmological models
and the astrophysically interesting static spherically symmetric models as well
as the stationary cylindrically symmetric models. The framework involves
methods for finding and exploiting hidden symmetries and invariant submanifolds
of the Hamiltonian formulation of the field equations. It unifies, simplifies
and extends most known work on hypersurface-homogeneous exact solutions. It is
shown that the same framework is also relevant to gravitational theories with a
similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for
publication in Phys. Rev.
The General Solution of Bianchi Type Vacuum Cosmology
The theory of symmetries of systems of coupled, ordinary differential
equations (ODE) is used to develop a concise algorithm in order to obtain the
entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs).
The symmetries used are the well known automorphisms of the Lie algebra for the
corresponding isometry group of each Bianchi Type, as well as the scaling and
the time re-parametrization symmetry. The application of the method to Type
VII_h results in (a) obtaining the general solution of Type VII_0 with the aid
of the third Painlev\'{e} transcendental (b) obtaining the general solution of
Type with the aid of the sixth Painlev\'{e} transcendental (c) the
recovery of all known solutions (six in total) without a prior assumption of
any extra symmetry (d) The discovery of a new solution (the line element given
in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like
hyper-surfaces, along with the emergence of the line element describing the
flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure
The Frenet Serret Description of Gyroscopic Precession
The phenomenon of gyroscopic precession is studied within the framework of
Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to
the congruence vorticity is highlighted with particular reference to the
irrotational congruence admitted by the stationary, axisymmetric spacetime.
General precession formulae are obtained for circular orbits with arbitrary
constant angular speeds. By successive reduction, different types of
precessions are derived for the Kerr - Schwarzschild - Minkowski spacetime
family. The phenomenon is studied in the case of other interesting spacetimes,
such as the De Sitter and G\"{o}del universes as well as the general
stationary, cylindrical, vacuum spacetimes.Comment: 37 pages, Paper in Late
Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment
We carry out a covariant calculation of the measurable relativistic effects
in an orbiting gyroscope experiment. The experiment, currently known as Gravity
Probe B, compares the spin directions of an array of spinning gyroscopes with
the optical axis of a telescope, all housed in a spacecraft that rolls about
the optical axis. The spacecraft is steered so that the telescope always points
toward a known guide star. We calculate the variation in the spin directions
relative to readout loops rigidly fixed in the spacecraft, and express the
variations in terms of quantities that can be measured, to sufficient accuracy,
using an Earth-centered coordinate system. The measurable effects include the
aberration of starlight, the geodetic precession caused by space curvature, the
frame-dragging effect caused by the rotation of the Earth and the deflection of
light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.
Generalized Quantum Theory of Recollapsing Homogeneous Cosmologies
A sum-over-histories generalized quantum theory is developed for homogeneous
minisuperspace type A Bianchi cosmological models, focussing on the particular
example of the classically recollapsing Bianchi IX universe. The decoherence
functional for such universes is exhibited. We show how the probabilities of
decoherent sets of alternative, coarse-grained histories of these model
universes can be calculated. We consider in particular the probabilities for
classical evolution defined by a suitable coarse-graining. For a restricted
class of initial conditions and coarse grainings we exhibit the approximate
decoherence of alternative histories in which the universe behaves classically
and those in which it does not. For these situations we show that the
probability is near unity for the universe to recontract classically if it
expands classically. We also determine the relative probabilities of
quasi-classical trajectories for initial states of WKB form, recovering for
such states a precise form of the familiar heuristic "J d\Sigma" rule of
quantum cosmology, as well as a generalization of this rule to generic initial
states.Comment: 41 pages, 4 eps figures, revtex 4. Modest revisions throughout.
Physics unchanged. To appear in Phys. Rev.
The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect
In the context of the natural splitting, the standard relative dynamics can
be expressed in terms of gravito-electromagnetic fields, which allow to
formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere
that this formal analogy can be used to derive the Sagnac effect in flat
space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize
those results to study the General Relativistic corrections to the Sagnac
effect in some stationary and axially symmetric geometries, such as the
space-time around a weakly gravitating and rotating source, Kerr space-time,
G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General
Relativity and Gravitatio
Gauged motion in general relativity and in Kaluza-Klein theories
In a recent paper [1] a new generalization of the Killing motion, the {\it
gauged motion}, has been introduced for stationary spacetimes where it was
shown that the physical symmetries of such spacetimes are well described
through this new symmetry. In this article after a more detailed study in the
stationary case we present the definition of gauged motion for general
spacetimes. The definition is based on the gauged Lie derivative induced by a
threading family of observers and the relevant reparametrization invariance. We
also extend the gauged motion to the case of Kaluza-Klein theories.Comment: 42 pages, revised version, typos correction along with some minor
changes, Revtex forma
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result