5,893 research outputs found
Collisions of rigidly rotating disks of dust in General Relativity
We discuss inelastic collisions of two rotating disks by using the
conservation laws for baryonic mass and angular momentum. In particular, we
formulate conditions for the formation of a new disk after the collision and
calculate the total energy loss to obtain upper limits for the emitted
gravitational energy.Comment: 30 pages, 9 figure
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
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
General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
In a recent paper we presented analytic expressions for the axis potential,
the disk metric, and the surface mass density of the global solution to
Einstein's field equations describing a rigidly rotating disk of dust. Here we
add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046
An Experimental Analysis of Optimal Renewable Resource Management: The Fishery
fishing industry;resource management;decision making;uncertainty;experimental economics
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
Non-existence of stationary two-black-hole configurations
We resume former discussions of the question, whether the spin-spin repulsion
and the gravitational attraction of two aligned black holes can balance each
other. To answer the question we formulate a boundary value problem for two
separate (Killing-) horizons and apply the inverse (scattering) method to solve
it. Making use of results of Manko, Ruiz and Sanabria-G\'omez and a novel black
hole criterion, we prove the non-existence of the equilibrium situation in
question.Comment: 15 pages, 3 figures; Contribution to Juergen Ehlers Memorial Issue
(GeRG journal
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
Estimating youth locomotion ground reaction forces using an accelerometer-based activity monitor.
To address a variety of questions pertaining to the interactions between physical activity, musculoskeletal loading and musculoskeletal health/injury/adaptation, simple methods are needed to quantify, outside a laboratory setting, the forces acting on the human body during daily activities. The purpose of this study was to develop a statistically based model to estimate peak vertical ground reaction force (pVGRF) during youth gait. 20 girls (10.9 ± 0.9 years) and 15 boys (12.5 ± 0.6 years) wore a Biotrainer AM over their right hip. Six walking and six running trials were completed after a standard warm-up. Average AM intensity (g) and pVGRF (N) during stance were determined. Repeated measures mixed effects regression models to estimate pVGRF from Biotrainer activity monitor acceleration in youth (girls 10-12, boys 12-14 years) while walking and running were developed. Log transformed pVGRF had a statistically significant relationship with activity monitor acceleration, centered mass, sex (girl), type of locomotion (run), and locomotion type-acceleration interaction controlling for subject as a random effect. A generalized regression model without subject specific random effects was also developed. The average absolute differences between the actual and predicted pVGRF were 5.2% (1.6% standard deviation) and 9% (4.2% standard deviation) using the mixed and generalized models, respectively. The results of this study support the use of estimating pVGRF from hip acceleration using a mixed model regression equation
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