5,194 research outputs found
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
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
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
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
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
- …