80 research outputs found
Matching of analytical and numerical solutions for neutron stars of arbitrary rotation
We demonstrate the results of an attempt to match the two-soliton analytical
solution with the numerically produced solutions of the Einstein field
equations, that describe the spacetime exterior of rotating neutron stars, for
arbitrary rotation. The matching procedure is performed by equating the first
four multipole moments of the analytical solution to the multipole moments of
the numerical one. We then argue that in order to check the effectiveness of
the matching of the analytical with the numerical solution we should compare
the metric components, the radius of the innermost stable circular orbit
(), the rotation frequency and the
epicyclic frequencies . Finally we present some
results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity
(NEB XIII), corrected typo in of eq. 5 of the published versio
Chaotic dynamics around astrophysical objects with nonisotropic stresses
The existence of chaotic behavior for the geodesics of the test particles
orbiting compact objects is a subject of much current research. Some years ago,
Gu\'eron and Letelier [Phys. Rev. E \textbf{66}, 046611 (2002)] reported the
existence of chaotic behavior for the geodesics of the test particles orbiting
compact objects like black holes induced by specific values of the quadrupolar
deformation of the source using as models the Erez--Rosen solution and the Kerr
black hole deformed by an internal multipole term. In this work, we are
interesting in the study of the dynamic behavior of geodesics around
astrophysical objects with intrinsic quadrupolar deformation or nonisotropic
stresses, which induces nonvanishing quadrupolar deformation for the
nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys.
Rev. Lett. \textbf{29} 1344 (1972)] and its arbitrary deformed generalization
obtained as the particular vacuum case of the five parametric solution of Manko
et al [Phys. Rev. D 62, 044048 (2000)], characterizing the geodesic dynamics
throughout the Poincar\'e sections method. In contrast to the results by
Gu\'eron and Letelier we find chaotic motion for oblate deformations instead of
prolate deformations. It opens the possibility that the particles forming the
accretion disk around a large variety of different astrophysical bodies
(nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also
conjecture that the existence of an arbitrary deformation parameter is
necessary for the existence of chaotic dynamics.Comment: 7 pages, 5 figure
Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star
A new six-parametric, axisymmetric and asymptotically flat exact solution of
Einstein-Maxwell field equations having reflection symmetry is presented. It
has arbitrary physical parameters of mass, angular momentum, mass--quadrupole
moment, current octupole moment, electric charge and magnetic dipole, so it can
represent the exterior field of a rotating, deformed, magnetized and charged
object; some properties of the closed-form analytic solution such as its
multipolar structure, electromagnetic fields and singularities are also
presented. In the vacuum case, this analytic solution is matched to some
numerical interior solutions representing neutron stars, calculated by Berti &
Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the
multipole moments be the same. As an independent test of accuracy of the
solution to describe exterior fields of neutron stars, we present an extensive
comparison of the radii of innermost stable circular orbits (ISCOs) obtained
from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett.
11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an
analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011
(1998)) and, our exact solution. We found that radii of ISCOs from our solution
fits better than others with realistic numerical interior solutions.Comment: 13 pages, 13 figures, LaTeX documen
Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: A prerequisite to compare metrics
We demonstrate how one should transform correctly quasi-isotropic coordinates
to Weyl-Papapetrou coordinates in order to compare the metric around a rotating
star that has been constructed numerically in the former coordinates with an
axially symmetric stationary metric that is given through an analytical form in
the latter coordinates. Since a stationary metric associated with an isolated
object that is built numerically partly refers to a non-vacuum solution
(interior of the star) the transformation of its coordinates to Weyl-Papapetrou
coordinates, which are usually used to describe vacuum axisymmetric and
stationary solutions of Einstein equations, is not straightforward in the
non-vacuum region. If this point is \textit{not} taken into consideration, one
may end up to erroneous conclusions about how well a specific analytical metric
matches the metric around the star, due to fallacious coordinate
transformations.Comment: 18 pages, 2 figure
Damping of quasi-2D internal wave attractors by rigid-wall friction
The reflection of internal gravity waves at sloping boundaries leads to
focusing or defocusing. In closed domains, focusing typically dominates and
projects the wave energy onto 'wave attractors'. For small-amplitude internal
waves, the projection of energy onto higher wave numbers by geometric focusing
can be balanced by viscous dissipation at high wave numbers. Contrary to what
was previously suggested, viscous dissipation in interior shear layers may not
be sufficient to explain the experiments on wave attractors in the classical
quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer
theory, we provide an elaborate description of the viscous dissipation in the
interior shear layer, as well as at the rigid boundaries. Our analysis shows
that even if the thin lateral Stokes boundary layers consist of no more than 1%
of the wall-to-wall distance, dissipation by lateral walls dominates at
intermediate wave numbers. Our extended model for the spectrum of 3D wave
attractors in equilibrium closes the gap between observations and theory by
Hazewinkel et al. (2008)
Equilibrium configurations of two charged masses in General Relativity
An asymptotically flat static solution of Einstein-Maxwell equations which
describes the field of two non-extreme Reissner - Nordstr\"om sources in
equilibrium is presented. It is expressed in terms of physical parameters of
the sources (their masses, charges and separating distance). Very simple
analytical forms were found for the solution as well as for the equilibrium
condition which guarantees the absence of any struts on the symmetry axis. This
condition shows that the equilibrium is not possible for two black holes or for
two naked singularities. However, in the case when one of the sources is a
black hole and another one is a naked singularity, the equilibrium is possible
at some distance separating the sources. It is interesting that for
appropriately chosen parameters even a Schwarzschild black hole together with a
naked singularity can be "suspended" freely in the superposition of their
fields.Comment: 4 pages; accepted for publication in Phys. Rev.
Exact solution for the simplest binary system of Kerr black holes
The full metric describing two counter-rotating identical Kerr black holes
separated by a massless strut is derived in the explicit analytical form. It
contains three arbitrary parameters which are the Komar mass M, Komar angular
momentum per unit mass a of one of the black holes (the other has the same mass
and equal but opposite angular momentum) and the coordinate distance R between
the centers of the horizons. In the limit of extreme black holes, the metric
becomes a special member of the Kinnersly-Chitre five-parameter family of
vacuum solutions generalizing the Tomimatsu-Sato delta=2 spacetime, and we
present the complete set of metrical fields defining this limit.Comment: 9 pages, 1 figure, typos corrected, a footnote on p.6 extende
Boundary layer on the surface of a neutron star
In an attempt to model the accretion onto a neutron star in low-mass X-ray
binaries, we present two-dimensional hydrodynamical models of the gas flow in
close vicinity of the stellar surface. First we consider a gas pressure
dominated case, assuming that the star is non-rotating. For the stellar mass we
take M_{\rm star}=1.4 \times 10^{-2} \msun and for the gas temperature K. Our results are qualitatively different in the case of a
realistic neutron star mass and a realistic gas temperature of
K, when the radiation pressure dominates. We show that to get the stationary
solution in a latter case, the star most probably has to rotate with the
considerable velocity.Comment: 7 pages, 7 figure
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