73 research outputs found
Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism
Conformally flat spacetimes with an elastic stress energy tensor given by a
diagonal trace-free anisotropic pressure tensor are investigated using 1+3
formalism. We show how the null tetrad Ricci components are related to the
pressure components and energy density. The 1+3 Bianchi and Jacobi identities
and Einstein field equations are written for this particular case. In general
the commutators must be considered since they supply potentially new
information on higher order derivatives of the 1+3 quantities. We solve the
system for the non rotating case which consist of ODEs of a spatial coordinate
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
Rotating elastic bodies in Einstein gravity
We prove that, given a stress-free, axially symmetric elastic body, there
exists, for sufficiently small values of the gravitational constant and of the
angular frequency, a unique stationary axisymmetric solution to the Einstein
equations coupled to the equations of relativistic elasticity with the body
performing rigid rotations around the symmetry axis at the given angular
frequency.Comment: 27 page
Charged black holes in compactified spacetimes
We construct and investigate a compactified version of the four-dimensional
Reissner-Nordstrom-NUT solution, generalizing the compactified Schwarzschild
black hole that has been previously studied by several workers. Our approach to
compactification is based on dimensional reduction with respect to the
stationary Killing vector, resulting in three-dimensional gravity coupled to a
nonlinear sigma model. Using that the original non-compactified solution
corresponds to a target space geodesic, the problem can be linearized much in
the same way as in the case of no electric nor NUT charge. An interesting
feature of the solution family is that for nonzero electric charge but
vanishing NUT charge, the solution has a curvature singularity on a torus that
surrounds the event horizon, but this singularity is removed when the NUT
charge is switched on. We also treat the Schwarzschild case in a more complete
way than has been done previously. In particular, the asymptotic solution (the
Levi-Civita solution with the height coordinate made periodic) has to our
knowledge only been calculated up to a determination of the mass parameter. The
periodic Levi-Civita solution contains three essential parameters, however, and
the remaining two are explicitly calculated here.Comment: 20 pages, 3 figures. v2: Typo corrected, reference adde
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
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