The Post-Newtonian Approximation of the Rigidly Rotating Disc of Dust to Arbitrary Order

Using the analytic, global solution for the rigidly rotating disc of dust as a starting point, an iteration scheme is presented for the calculation of an arbitrary coefficient in the post-Newtonian (PN) approximation of this solution. The coefficients were explicitly calculated up to the 12th PN level and are listed in this paper up to the 4th PN level. The convergence of the series is discussed and the approximation is found to be reliable even in highly relativistic cases. Finally, the ergospheres are calculated at increasing orders of the approximation and for increasingly relativistic situations.Comment: 19 pages, 2 tables, 4 figures Accepted for publication in Phys. Rev.

Differentially rotating disks of dust

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Baecklund transformations to appropriate seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and Gravitation". Second version with minor correction

Non-existence of stationary two-black-hole configurations: The degenerate case

In a preceding paper we examined the question whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure

The comet rendezvous asteroid flyby mission: A status report

The Comet Rendezvous Asteroid Flyby (CRAF) mission received a new start in fiscal year 1990. CRAF will match orbits with an active short-period comet and follow it around the Sun, making scientific measurements of the nucleus, coma, and tail. The Imaging system will map the nucleus surface at a resolution of 1 meter/line-pair or better, while Visible and Infrared Mapping Spectrometer (VIMS) and Thermal Infrared Radiometer Experiment (TIREX) will produce spectral and thermal maps of the surface. Onboard instruments will collect cometary dust, ice, and gases and perform elemental and molecular analysis. A suite of fields and particles instruments will observe the solar wind interaction with the cometary atmosphere and tail. Radio tracking of the spacecraft will provide an accurate measure of the nucleus mass and higher harmonics in the comet's gravity field. En route to the comet, the spacecraft will make a close flyby of a large asteroid, preferably a primitive type from the outer main belt. Observations at the asteroid include remote sensing mapping of the surface, detection of any solar wind interaction observable at the flyby distance, and measurement of the asteroid mass to better than 10 percent accuracy. Detailed design of the CRAF spacecraft is currently underway at the Jet Propulsion Laboratory (JPL). Recent mass growth has necessitated a switch to Venus-Earth gravity assist type trajectories, similar to that used by the Galileo spacecraft. These trajectories require longer flight times from launch to rendezvous with the target comet. The details of the current baseline mission, spacecraft design, and instrument payload will be reviewed

Differentially rotating disks of dust: Arbitrary rotation law

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentially rotating disk of dust, for which a continuous transition to some Newtonian disk exists. It will be shown how for given boundary conditions (i. e. proper surface mass density or angular velocity of the disk) the gravitational field can be approximated in terms of the above solutions. Furthermore, particular examples will be discussed, including disks with a realistic profile for the angular velocity and more exotic disks possessing two spatially separated ergoregions.Comment: 23 pages, 3 figures, submitted to 'General Relativity and Gravitation

Dirichlet Boundary Value Problems of the Ernst Equation

We demonstrate how the solution to an exterior Dirichlet boundary value problem of the axisymmetric, stationary Einstein equations can be found in terms of generalized solutions of the Backlund type. The proof that this generalization procedure is valid is given, which also proves conjectures about earlier representations of the gravitational field corresponding to rotating disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in equation (4

On the black hole limit of rotating discs and rings

Solutions to Einstein's field equations describing rotating fluid bodies in equilibrium permit parametric (i.e. quasi-stationary) transitions to the extreme Kerr solution (outside the horizon). This has been shown analytically for discs of dust and numerically for ring solutions with various equations of state. From the exterior point of view, this transition can be interpreted as a (quasi) black hole limit. All gravitational multipole moments assume precisely the values of an extremal Kerr black hole in the limit. In the present paper, the way in which the black hole limit is approached is investigated in more detail by means of a parametric Taylor series expansion of the exact solution describing a rigidly rotating disc of dust. Combined with numerical calculations for ring solutions our results indicate an interesting universal behaviour of the multipole moments near the black hole limit.Comment: 18 pages, 4 figures; Dedicated to Gernot Neugebauer on the occasion of his 70th birthda

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table

Ion mass spectrometer

An ion mass spectrometer is described which detects and indicates the characteristics of ions received over a wide angle, and which indicates the mass to charge ratio, the energy, and the direction of each detected ion. The spectrometer includes a magnetic analyzer having a sector magnet that passes ions received over a wide angle, and an electrostatic analyzer positioned to receive ions passing through the magnetic analyzer. The electrostatic analyzer includes a two dimensional ion sensor at one wall of the analyzer chamber, that senses not only the lengthwise position of the detected ion to indicate its mass to charge ratio, but also detects the ion position along the width of the chamber to indicate the direction in which the ion was traveling