53 research outputs found
Magneto-elastic torsional oscillations of magnetars
We extend a general-relativistic ideal magneto-hydrodynamical code to include
the effects of elasticity. Using this numerical tool we analyse the
magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In
simulations without magnetic field we are able to recover the purely crustal
shear oscillations within an accuracy of about a few per cent. For dipole
magnetic fields between 5 x 10^13 and 10^15 G the Alfv\'en oscillations become
modified substantially by the presence of the crust. Those quasi-periodic
oscillations (QPOs) split into three families: Lower QPOs near the equator,
Edge QPOs related to the last open field line and Upper QPOs at larger distance
from the equator. Edge QPOs are called so because they are related to an edge
in the corresponding Alfv\'en continuum. The Upper QPOs are of the same kind,
while the Lower QPOs are turning-point QPOs, related to a turning point in the
continuous spectrum.Comment: 6 pages, 1 figure, 1 table, Proceedings of NEB14, to appear in J.
Phys.: Conf. Se
A unified treatment of cubic invariants at fixed and arbitrary energy
Cubic invariants for two-dimensional Hamiltonian systems are investigated
using the Jacobi geometrization procedure. This approach allows for a unified
treatment of invariants at both fixed and arbitrary energy. In the geometric
picture the invariant generally corresponds to a third rank Killing tensor,
whose existence at a fixed energy value forces the metric to satisfy a
nonlinear integrability condition expressed in terms of a Kahler potential.
Further conditions, leading to a system of equations which is overdetermined
except for singular cases, are added when the energy is arbitrary. As solutions
to these equations we obtain several new superintegrable cases in addition to
the previously known cases. We also discover a superintegrable case where the
cubic invariant is of a new type which can be represented by an energy
dependent linear invariant. A complete list of all known systems which admit a
cubic invariant at arbitrary energy is given.Comment: 16 pages, LaTeX2e, slightly revised version. To appear in J. Math.
Phys. vol 41, pp 370-384 (2000
Elastic Stars in General Relativity: II. Radial perturbations
We study radial perturbations of general relativistic stars with elastic
matter sources. We find that these perturbations are governed by a second order
differential equation which, along with the boundary conditions, defines a
Sturm-Liouville type problem that determines the eigenfrequencies. Although
some complications arise compared to the perfect fluid case, leading us to
consider a generalisation of the standard form of the Sturm-Liouville equation,
the main results of Sturm-Liouville theory remain unaltered. As an important
consequence we conclude that the mass-radius curve for a one-parameter sequence
of regular equilibrium models belonging to some particular equation of state
can be used in the same well-known way as in the perfect fluid case, at least
if the energy density and the tangential pressure of the background solutions
are continuous. In particular we find that the fundamental mode frequency has a
zero for the maximum mass stars of the models with solid crusts considered in
Paper I of this series.Comment: 22 pages, no figures, final version accepted for publication in
Class. Quantum Grav. The treatment of the junction conditions has been
improve
Spherically symmetric elasticity in relativity
The relativistic theory of elasticity is reviewed within the spherically symmetric
context with a view towards the modelling of star interiors possessing elastic properties such as
the ones expected in neutron stars. Emphasis is placed on generality in the main sections of the
paper, and the results are then applied to specific examples. Along the way, a few general results
for spacetimes admitting isometries are deduced, and their consequences are fully exploited in
the case of spherical symmetry relating them next to the the case in which the material content
of the spacetime is some elastic material. This paper extends and generalizes the pioneering
work by Magli and Kijowski [1], Magli [2] and [3], and complements, in a sense, that by Karlovini
and Samuelsson in their interesting series of papers [4], [5] and [6].JC acknowledges financial support from MEC through grant No.: HP2006-0074. Partial financial support from (MEC) through grant FPA-2007-60220 and from the Govern de les Illes Balears is also acknowledged. IB and EGLRV acknowledge financial support from (CRUP) through grant No.: E-89/07 and from FCT and CMAT
The static spherically symmetric body in relativistic elasticity
In this paper is discussed a class of static spherically symmetric solutions
of the general relativistic elasticity equations. The main point of discussion
is the comparison of two matter models given in terms of their stored energy
functionals, i.e., the rule which gives the amount of energy stored in the
system when it is deformed. Both functionals mimic (and for small deformations
approximate) the classical Kirchhoff-St.Venant materials but differ in the
strain variable used. We discuss the behavior of the systems for large
deformations.Comment: 19 pages, 8 figure
General spherically symmetric elastic stars in Relativity
The relativistic theory of elasticity is reviewed within the spherically
symmetric context with a view towards the modeling of star interiors possessing
elastic properties such as theones expected in neutron stars. Emphasis is
placed on generality in the main sections of the paper, and the results are
then applied to specific examples. Along the way, a few general results for
spacetimes admitting isometries are deduced, and their consequences are fully
exploited in the case of spherical symmetry relating them next to the the case
in which the material content of the spacetime is some elastic material. This
paper extends and generalizes the pioneering work by Magli and Kijowski [1],
Magli [2] and [3], and complements, in a sense, that by Karlovini and
Samuelsson in their interesting series of papers [4], [5] and [6].Comment: 23 page
Analysing the elasticity difference tensor of general relativity
The elasticity difference tensor, used in [1] to describe elasticity
properties of a continuous medium filling a space-time, is here analysed from
the point of view of the space-time connection. Principal directions associated
with this tensor are compared with eigendirections of the material metric.
Examples concerning spherically symmetric and axially symmetric space-times are
then presented.Comment: 17 page
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