Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium

The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition implies that the fluid flow moves only along the angular direction, i.e. there is no convection. Using this simplification, some recent studies have provided us with uniqueness and existence results for asymptotically flat vacuum exterior fields given the interior sources. Here, the generalisation of the problem to include general sources is studied. It is proven that the convective motions have no direct influence on the exterior field, and hence, that the aforementioned results on uniqueness and existence of exterior fields apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum Gra

Magnetically Driven Warping, Precession and Resonances in Accretion Disks

The inner region of the accretion disk onto a rotating magnetized central star (neutron star, white dwarf or T Tauri star) is subjected to magnetic torques which induce warping and precession of the disk. The origin of these torques lies in the interaction between the (induced) surface current on the disk and the horizontal magnetic field (parallel to the disk) produced by the inclined magnetic dipole. Under quite general conditions, there exists a magnetic warping instability in which the magnetic torque drives the disk plane away from the equatorial plane of the star toward a state where the disk normal vector is perpendicular to the spin axis. Viscous stress tends to suppress the warping instability at large radii, but the magnetic torque always dominates as the disk approaches the magnetosphere boundary. The magnetic torque also drives the tilted inner disk into retrograde precession around the stellar spin axis. Moreover, resonant magnetic forcing on the disk can occur which may affect the dynamics of the disk. The magnetically driven warping instability and precession may be related to a number observational puzzles, including: (1) Spin evolution (torque reversal) of accreting X-ray pulsars; (2) Quasi-periodic oscillations in low-mass X-ray binaries; (3) Super-orbital periods in X-ray binaries; (4) Photometric period variations of T Tauri stars.Comment: 39 pages including 1 ps figure; Published version; ApJ, 524, 1030-1047 (1999

Non--linear magnetic field decay in neutron stars -- Theory and observations

There exists both theoretical and observational evidence that the magnetic field decay in neutron stars may proceed in a pronounced non--linear way during a certain episode of the neutron star's life. In the presence of a strong magnetic field the Hall--drift dominates the field evolution in the crust and/or the superfluid core of neutron stars. Analysing observations of $P$ and $\dot{P}$ for sufficiently old isolated pulsars we gain strong hints for a significantly non--linear magnetic field decay. Under certain conditions with respect to the geometry and strength of a large--scale magnetic background field an instability is shown to occur which rapidly raises small--scale magnetic field modes. Their growth rates increase with the background field strength and may reach $\sim 10^4$ times the ohmic decay rate. Consequences for the rotational and thermal evolution as well as for the cracking of the crust of neutron stars are discussed.Comment: 11 pages, 8 figures, accepted by `Astronomy & Astrophysics

General Relativistic 1+3 Orthonormal Frame Approach Revisited

The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain a number of interesting problems by specializing the general equations. In particular, equation systems for ``silent'' dust cosmological models also containing magnetic Maxwell fields, locally rotationally symmetric spacetime geometries and spatially homogeneous cosmological models are presented. We show that while the 3-Cotton--York tensor is zero for Szekeres dust models, it is nonzero for a generic representative within the ``silent'' class.Comment: 41 pages, uufiles encoded postscript file, submitted to Phys. Rev.

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl

Homothetic perfect fluid space-times

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group $H_4$ (acting multiply transitively) and $H_3$. A classification of all possible Lie algebra structures along with (local) coordinate expressions for the metric and homothetic vectors is then provided (irrespectively of the matter content), and some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra

Description of the Scenario Machine

We present here an updated description of the "Scenario Machine" code. This tool is used to carry out a population synthesis of binary stars. Previous version of the description can be found at http://xray.sai.msu.ru/~mystery//articles/review/contents.htmlComment: 32 pages, 3 figures. Corrected typo