32 research outputs found
Measuring multipole moments of Weyl metrics by means of gyroscopes
Using the technique of Rindler and Perlick we calculate the total precession
per revolution of a gyroscope circumventing the source of Weyl metrics. We
establish thereby a link between the multipole moments of the source and an
``observable'' quantity. Special attention deserves the case of the
gamma-metric. As an extension of this result we also present the corresponding
expressions for some stationary space-times.Comment: 18 pages Latex, To appear in J.Math.Phy
Approximate gravitational field of a rotating deformed mass
A new approximate solution of vacuum and stationary Einstein field equations
is obtained. This solution is constructed by means of a power series expansion
of the Ernst potential in terms of two independent and dimensionless parameters
representing the quadrupole and the angular momentum respectively. The main
feature of the solution is a suitable description of small deviations from
spherical symmetry through perturbations of the static configuration and the
massive multipole structure by using those parameters. This quality of the
solution might eventually provide relevant differences with respect to the
description provided by the Kerr solution.Comment: 16 pages. Latex. To appear in General Relativity and Gravitatio
A source of a quasi--spherical space--time: The case for the M--Q solution
We present a physically reasonable source for an static, axially--symmetric
solution to the Einstein equations. Arguments are provided, supporting our
belief that the exterior space--time produced by such source, describing a
quadrupole correction to the Schwarzschild metric, is particularly suitable
(among known solutions of the Weyl family) for discussing the properties of
quasi--spherical gravitational fields.Comment: 34 pages, 9 figures. To appear in GR
Static axisymmetric space-times with prescribed multipole moments
In this article we develop a method of finding the static axisymmetric
space-time corresponding to any given set of multipole moments. In addition to
an implicit algebraic form for the general solution, we also give a power
series expression for all finite sets of multipole moments. As conjectured by
Geroch we prove in the special case of axisymmetry, that there is a static
space-time for any given set of multipole moments subject to a (specified)
convergence criterion. We also use this method to confirm a conjecture of
Hernandez-Pastora and Martin concerning the monopole-quadropole solution.Comment: 14 page
From geodesics of the multipole solutions to the perturbed Kepler problem
A static and axisymmetric solution of the Einstein vacuum equations with a
finite number of Relativistic Multipole Moments (RMM) is written in MSA
coordinates up to certain order of approximation, and the structure of its
metric components is explicitly shown. From the equation of equatorial
geodesics we obtain the Binet equation for the orbits and it allows us to
determine the gravitational potential that leads to the equivalent classical
orbital equations of the perturbed Kepler problem. The relativistic corrections
to Keplerian motion are provided by the different contributions of the RMM of
the source starting from the Monopole (Schwarzschild correction). In
particular, the perihelion precession of the orbit is calculated in terms of
the quadrupole and 2-pole moments. Since the MSA coordinates generalize the
Schwarzschild coordinates, the result obtained allows measurement of the
relevance of the quadrupole moment in the first order correction to the
perihelion frequency-shift