393 research outputs found
Features of the extreme events observed in the all-solid state laser with a saturable absorber
Extreme events (sometimes also called optical rogue waves), in the form of
pulses of extraordinary intensity, are easily observed in its chaotic regime if
the Fresnel number of the cavity is high. This result suggests that the
nonlinear interaction among transverse modes is an essential ingredient in the
formation of extreme events in this type of lasers, but there is no theoretical
description of the phenomenon yet. We report here a set of experimental results
on the regularities of these extreme events, to provide a basis for the
development of such a description. Among these results, we point out here: i)
the decay of the correlation across the transversal section of the laser beam,
and ii) the appearance of extreme events even if the time elapsed since the
previous pulse is relatively short (in terms of the average inter-pulse
separation), what indicates the existence of some unknown mechanism of energy
storage. We hypothesize that this mechanism is related with the imperfect
depletion of the gain by some of the transversal modes. We also present
evidence in support of this hypothesis.Comment: 9 pages, 9 figure
Numerical models of irrotational binary neutron stars in general relativity
We report on general relativistic calculations of quasiequilibrium
configurations of binary neutron stars in circular orbits with zero vorticity.
These configurations are expected to represent realistic situations as opposed
to corotating configurations. The Einstein equations are solved under the
assumption of a conformally flat spatial 3-metric (Wilson-Mathews
approximation). The velocity field inside the stars is computed by solving an
elliptical equation for the velocity scalar potential. Results are presented
for sequences of constant baryon number (evolutionary sequences). Although the
central density decreases much less with the binary separation than in the
corotating case, it still decreases. Thus, no tendency is found for the stars
to individually collapse to black hole prior to merger.Comment: Minor corrections, improved figure, 5 pages, REVTeX, Phys. Rev. Lett.
in pres
Binary black holes in circular orbits. II. Numerical methods and first results
We present the first results from a new method for computing spacetimes
representing corotating binary black holes in circular orbits. The method is
based on the assumption of exact equilibrium. It uses the standard 3+1
decomposition of Einstein equations and conformal flatness approximation for
the 3-metric. Contrary to previous numerical approaches to this problem, we do
not solve only the constraint equations but rather a set of five equations for
the lapse function, the conformal factor and the shift vector. The orbital
velocity is unambiguously determined by imposing that, at infinity, the metric
behaves like the Schwarzschild one, a requirement which is equivalent to the
virial theorem. The numerical scheme has been implemented using multi-domain
spectral methods and passed numerous tests. A sequence of corotating black
holes of equal mass is calculated. Defining the sequence by requiring that the
ADM mass decrease is equal to the angular momentum decrease multiplied by the
orbital angular velocity, it is found that the area of the apparent horizons is
constant along the sequence. We also find a turning point in the ADM mass and
angular momentum curves, which may be interpreted as an innermost stable
circular orbit (ISCO). The values of the global quantities at the ISCO,
especially the orbital velocity, are in much better agreement with those from
third post-Newtonian calculations than with those resulting from previous
numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the
regularization procedure for the shift vector, new section devoted to the
check of the momentum constraint, references added + minor corrections,
accepted for publication in Phys. Rev.
Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy
For general relativistic equilibrium stellar models (stationary axisymmetric
asymptotically flat and convection-free) with differential rotation, it is
shown that for a wide class of rotation laws the distribution of angular
velocity of the fluid has a sign, say "positive", and then both the dragging
rate and the angular momentum density are positive. In addition, the "mean
value" (with respect to an intrinsic density) of the dragging rate is shown to
be less than the mean value of the fluid angular velocity (in full general,
without having to restrict the rotation law, nor the uniformity in sign of the
fluid angular velocity); this inequality yields the positivity and an upper
bound of the total rotational energy.Comment: 23 pages, no figures, LaTeX. Submitted to J. Math. Phy
Relativistic stars with purely toroidal magnetic fields
We investigate the effects of the purely toroidal magnetic field on the
equilibrium structures of the relativistic stars. The master equations for
obtaining equilibrium solutions of relativistic rotating stars containing
purely toroidal magnetic fields are derived for the first time. To solve these
master equations numerically, we extend the Cook-Shapiro-Teukolsky scheme for
calculating relativistic rotating stars containing no magnetic field to
incorporate the effects of the purely toroidal magnetic fields. By using the
numerical scheme, we then calculate a large number of the equilibrium
configurations for a particular distribution of the magnetic field in order to
explore the equilibrium properties. We also construct the equilibrium sequences
of the constant baryon mass and/or the constant magnetic flux, which model the
evolution of an isolated neutron star as it loses angular momentum via the
gravitational waves. Important properties of the equilibrium configurations of
the magnetized stars obtained in this study are summarized as follows ; (1) For
the non-rotating stars, the matter distribution of the stars is prolately
distorted due to the toroidal magnetic fields. (2) For the rapidly rotating
stars, the shape of the stellar surface becomes oblate because of the
centrifugal force. But, the matter distribution deep inside the star is
sufficiently prolate for the mean matter distribution of the star to be
prolate. (3) The stronger toroidal magnetic fields lead to the mass-shedding of
the stars at the lower angular velocity. (4) For some equilibrium sequences of
the constant baryon mass and magnetic flux, the stars can spin up as they lose
angular momentum.Comment: 13 figures, 7 tables, submitted to PR
Relativistic virialization in the Spherical Collapse model for Einstein-de Sitter and \Lambda CDM cosmologies
Spherical collapse has turned out to be a successful semi-analytic model to
study structure formation in different DE models and theories of gravity.
Nevertheless, the process of virialization is commonly studied on the basis of
the virial theorem of classical mechanics. In the present paper, a fully
generally-relativistic virial theorem based on the Tolman-Oppenheimer-Volkoff
(TOV) solution for homogeneous, perfect-fluid spheres is constructed for the
Einstein-de Sitter and \Lambda CDM cosmologies. We investigate the accuracy of
classical virialization studies on cosmological scales and consider
virialization from a more fundamental point of view. Throughout, we remain
within general relativity and the class of FLRW models. The virialization
equation is set up and solved numerically for the virial radius, y_{vir}, from
which the virial overdensity \Delta_{V} is directly obtained. Leading order
corrections in the post-Newtonian framework are derived and quantified. In
addition, problems in the application of this formalism to dynamical DE models
are pointed out and discussed explicitly. We show that, in the weak field
limit, the relative contribution of the leading order terms of the
post-Newtonian expansion are of the order of 10^{-3}% and the solution of Wang
& Steinhardt (1998) is precisely reproduced. Apart from the small corrections,
the method could provide insight into the process of virialization from a more
fundamental point of view.Comment: 15 pages, 2 figure
Testing a Simplified Version of Einstein's Equations for Numerical Relativity
Solving dynamical problems in general relativity requires the full machinery
of numerical relativity. Wilson has proposed a simpler but approximate scheme
for systems near equilibrium, like binary neutron stars. We test the scheme on
isolated, rapidly rotating, relativistic stars. Since these objects are in
equilibrium, it is crucial that the approximation work well if we are to
believe its predictions for more complicated systems like binaries. Our results
are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107
Irrotational binary neutron stars in quasiequilibrium
We report on numerical results from an independent formalism to describe the
quasi-equilibrium structure of nonsynchronous binary neutron stars in general
relativity. This is an important independent test of controversial numerical
hydrodynamic simulations which suggested that nonsynchronous neutron stars in a
close binary can experience compression prior to the last stable circular
orbit. We show that, for compact enough stars the interior density increases
slightly as irrotational binary neutron stars approach their last orbits. The
magnitude of the effect, however, is much smaller than that reported in
previous hydrodynamic simulations.Comment: 4 pages, 2 figures, revtex, accepted for publication in Phys. Rev.
Black Holes Surrounded by Uniformly Rotating Rings
Highly accurate numerical solutions to the problem of Black Holes surrounded
by uniformly rotating rings in axially symmetric, stationary spacetimes are
presented. The numerical methods developed to handle the problem are discussed
in some detail. Related Newtonian problems are described and numerical results
provided, which show that configurations can reach an inner mass-shedding limit
as the mass of the central object increases. Exemplary results for the full
relativistic problem for rings of constant density are given and the
deformation of the event horizon due to the presence of the ring is
demonstrated. Finally, we provide an example of a system for which the angular
momentum of the central Black Hole divided by the square of its mass exceeds
one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected,
corresponds to version in PR
Equilibrium Configurations of Strongly Magnetized Neutron Stars with Realistic Equations of State
We investigate equilibrium sequences of magnetized rotating stars with four
kinds of realistic equations of state (EOSs) of SLy (Douchin et al.), FPS
(Pandharipande et al.), Shen (Shen et al.), and LS (Lattimer & Swesty).
Employing the Tomimura-Eriguchi scheme to construct the equilibrium
configurations. we study the basic physical properties of the sequences in the
framework of Newton gravity. In addition we newly take into account a general
relativistic effect to the magnetized rotating configurations. With these
computations, we find that the properties of the Newtonian magnetized stars,
e.g., structure of magnetic field, highly depends on the EOSs.
The toroidal magnetic fields concentrate rather near the surface for Shen and
LS EOSs than those for SLy and FPS EOSs. The poloidal fields are also affected
by the toroidal configurations. Paying attention to the stiffness of the EOSs,
we analyze this tendency in detail. In the general relativistic stars, we find
that the difference due to the EOSs becomes small because all the employed EOSs
become sufficiently stiff for the large maximum density, typically greater than
. The maximum baryon mass of the magnetized stars
with axis ratio increases about up to twenty percents for that of
spherical stars. We furthermore compute equilibrium sequences at finite
temperature, which should serve as an initial condition for the hydrodynamic
study of newly-born magnetars. Our results suggest that we may obtain
information about the EOSs from the observation of the masses of magnetars.Comment: submitted to MNRA
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