3,451 research outputs found
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
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
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
Geodesics in a quasispherical spacetime: A case of gravitational repulsion
Geodesics are studied in one of the Weyl metrics, referred to as the M--Q
solution. First, arguments are provided, supporting our belief that this
space--time is the more suitable (among the known solutions of the Weyl family)
for discussing the properties of strong quasi--spherical gravitational fields.
Then, the behaviour of geodesics is compared with the spherically symmetric
situation, bringing out the sensitivity of the trajectories to deviations from
spherical symmetry. Particular attention deserves the change of sign in proper
radial acceleration of test particles moving radially along symmetry axis,
close to the surface, and related to the quadrupole moment of the
source.Comment: 30 pages late
Long-term segmentation-free assessment of head-flagellum movement and intracellular calcium in swimming human sperm
The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy
We calculate the instantaneous proper radial acceleration of test particles
(as measured by a locally defined Lorentzian observer) in a Weyl spacetime,
close to the horizon. As expected from the Israel theorem, there appear some
bifurcations with respect to the spherically symmetric case (Schwarzschild),
which are explained in terms of the behaviour of the superenergy, bringing out
the physical relevance of this quantity in the study of general relativistic
systems.Comment: 14 pages, Latex. 4 figures. New references added. Typos corrected. To
appear in Int. J. Theor. Phy
Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity
We show that it is possible to obtain credible static anisotropic spherically
symmetric matter configurations starting from known density profiles and
satisfying a nonlocal equation of state. These particular types of equation of
state describe, at a given point, the components of the corresponding
energy-momentum tensor not only as a function at that point, but as a
functional throughout the enclosed configuration. To establish the physical
plausibility of the proposed family of solutions satisfying nonlocal equation
of state, we study the constraints imposed by the junction and energy
conditions on these bounded matter distributions.
We also show that it is possible to obtain physically plausible static
anisotropic spherically symmetric matter configurations, having nonlocal
equations of state\textit{,}concerning the particular cases where the radial
pressure vanishes and, other where the tangential pressures vanishes. The later
very particular type of relativistic sphere with vanishing tangential stresses
is inspired by some of the models proposed to describe extremely magnetized
neutron stars (magnetars) during the transverse quantum collapse.Comment: 21 pages, 1 figure, minor changes in the text, references added, two
new solutions studie
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