49 research outputs found
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)
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
Nodal and Periastron Precession of Inclined Orbits in the Field of a Rapidly Rotating Neutron Star
We derive a formula for the nodal precession frequency and the Keplerian
period of a particle at an arbitrarily inclined orbit (with a minimum
latitudinal angle reached at the orbit) in the post-Newtonian approximation in
the external field of an oblate rotating neutron star (NS). We also derive
formulas for the nodal precession and periastron rotation frequencies of
slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS
in the form of asymptotic expansions whose first terms are given by the
Okazaki--Kato formulas. The NS gravitational field is described by the exact
solution of the Einstein equation that includes the NS quadrupole moment
induced by rapid rotation. Convenient asymptotic formulas are given for the
metric coefficients of the corresponding space-time in the form of Kerr metric
perturbations in Boyer--Lindquist coordinates.Comment: 12 page
The rotation curve and mass-distribution in highly flattened galaxies
A new method is developed which permits the reconstruction of the
surface-density distribution in the galactic disk of finite radius from an
arbitrary smooth distribution of the angular velocity via two simple
quadratures. The existence of upper limits for disk's mass and radius during
the analytic continuation of rotation curves into the hidden (non-radiating)
part of the disk is demonstrated.Comment: 13 pages, 2 figure
How can exact and approximate solutions of Einstein's field equations be compared?
The problem of comparison of the stationary axisymmetric vacuum solutions
obtained within the framework of exact and approximate approaches for the
description of the same general relativistic systems is considered. We suggest
two ways of carrying out such comparison: (i) through the calculation of the
Ernst complex potential associated with the approximate solution whose form on
the symmetry axis is subsequently used for the identification of the exact
solution possessing the same multipole structure, and (ii) the generation of
approximate solutions from exact ones by expanding the latter in series of
powers of a small parameter. The central result of our paper is the derivation
of the correct approximate analogues of the double-Kerr solution possessing the
physically meaningful equilibrium configurations. We also show that the
interpretation of an approximate solution originally attributed to it on the
basis of some general physical suppositions may not coincide with its true
nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure
Integrability of generalized (matrix) Ernst equations in string theory
The integrability structures of the matrix generalizations of the Ernst
equation for Hermitian or complex symmetric -matrix Ernst potentials
are elucidated. These equations arise in the string theory as the equations of
motion for a truncated bosonic parts of the low-energy effective action
respectively for a dilaton and - matrix of moduli fields or for a
string gravity model with a scalar (dilaton) field, U(1) gauge vector field and
an antisymmetric 3-form field, all depending on two space-time coordinates
only. We construct the corresponding spectral problems based on the
overdetermined -linear systems with a spectral parameter and the
universal (i.e. solution independent) structures of the canonical Jordan forms
of their matrix coefficients. The additionally imposed conditions of existence
for each of these systems of two matrix integrals with appropriate symmetries
provide a specific (coset) structures of the related matrix variables. An
equivalence of these spectral problems to the original field equations is
proved and some approach for construction of multiparametric families of their
solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop
``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004,
Gallipoli (Lecce), Italy. Minor typos, language and references corrections.
To be published in the proceedings in Theor. Math. Phy
Nodal and Periastron Precession of Inclined Orbits in the Field of a Rotating Black Hole
The inclination of low-eccentricity orbits is shown to significantly affect
the orbital parameters, in particular, the Keplerian, nodal precession, and
periastron rotation frequencies, which are interpreted in terms of observable
quantities. For the nodal precession and periastron rotation frequencies of
low-eccentricity orbits in a Kerr field, we derive a Taylor expansion in terms
of the Kerr parameter at arbitrary orbital inclinations to the black-hole spin
axis and at arbitrary radial coordinates. The particle radius, energy, and
angular momentum in the marginally stable circular orbits are calculated as
functions of the Kerr parameter and parameter in the form of Taylor
expansions in terms of to within . By analyzing our numerical
results, we give compact approximation formulas for the nodal precession
frequency of the marginally stable circular orbits at various in the entire
range of variation of Kerr parameter.Comment: 18 pages, to be published in Astronomy Letters, 2001, vol 27 (12
Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
For the fields depending on two of the four space-time coordinates only, the
spaces of local solutions of various integrable reductions of Einstein's field
equations are shown to be the subspaces of the spaces of local solutions of the
``null-curvature'' equations constricted by a requirement of a universal (i.e.
solution independent) structures of the canonical Jordan forms of the unknown
matrix variables. These spaces of solutions of the ``null-curvature'' equations
can be parametrized by a finite sets of free functional parameters -- arbitrary
holomorphic (in some local domains) functions of the spectral parameter which
can be interpreted as the monodromy data on the spectral plane of the
fundamental solutions of associated linear systems. Direct and inverse problems
of such mapping (``monodromy transform''), i.e. the problem of finding of the
monodromy data for any local solution of the ``null-curvature'' equations with
given canonical forms, as well as the existence and uniqueness of such solution
for arbitrarily chosen monodromy data are shown to be solvable unambiguously.
The linear singular integral equations solving the inverse problems and the
explicit forms of the monodromy data corresponding to the spaces of solutions
of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction