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

Equilibrium Configurations of Homogeneous Fluids in General Relativity

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and two-ring solutions. Combining our knowledge of the first four classes with post-Newtonian results and the Newtonian portion of the first ten classes, we present the qualitative behaviour of the entire relativistic solution space. The Newtonian disc limit can only be reached by going through infinitely many of the aforementioned classes. Only once this limiting process has been consummated, can one proceed again into the relativistic regime and arrive at the analytically known relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference, accepted by MNRA

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

Magnetic field reversals and galactic dynamos

We argue that global magnetic field reversals similar to those observed in the Milky Way occur quite frequently in mean-field galactic dynamo models that have relatively strong, random, seed magnetic fields that are localized in discrete regions. The number of reversals decreases to zero with reduction of the seed strength, efficiency of the galactic dynamo and size of the spots of the seed field. A systematic observational search for magnetic field reversals in a representative sample of spiral galaxies promises to give valuable information concerning seed magnetic fields and, in this way, to clarify the initial stages of galactic magnetic field evolution

Nb3Sn wire shape and cross sectional area inhomogeneity in Rutherford cables

During Rutherford cable production the wires are plastically deformed and their initially round shape is distorted. Using X-ray absorption tomography we have determined the 3D shape of an unreacted Nb3Sn 11 T dipole Rutherford cable, and of a reacted and impregnated Nb3Sn cable double stack. State-of-the-art image processing was applied to correct for tomographic artefacts caused by the large cable aspect ratio, for the segmentation of the individual wires and subelement bundles inside the wires, and for the calculation of the wire cross sectional area and shape variations. The 11 T dipole cable cross section oscillates by 2% with a frequency of 1.24 mm (1/80 of the transposition pitch length of the 40 wire cable). A comparatively stronger cross sectional area variation is observed in the individual wires at the thin edge of the keystoned cable where the wire aspect ratio is largest.Comment: 6 pages, 11 figures, presented at EUCAS 201

Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes

We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of dust surrounded by such a ring. Both types of spacetime are regular everywhere (outside of the horizon in the case of the black hole) and fulfil the requirements of the positive energy theorem. However, it is shown that both the black hole and the disc can have negative Komar mass. Furthermore, there exists a continuous transition from discs to black holes even when their Komar masses are negative.Comment: 7 pages, 2 figures, document class iopart. v2: changes made (including title) to coincide with published versio

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

Intercomparison of ground-based and space solar flux measurements

Detailed temporal measurements of the solar flux at one location are performed. These data are then analyzed and compared to the potential of space measurements which allow one to consider the flux falling on areas of the earth. An important result of the research is that the temporal characteristics of the flux in the presence of a real atmosphere would be difficult to obtain from space and that the variations in the flux can be highly significant in regard to most solar conversion schemes. The detailed results of the research are presented. The instruments developed to separate the direct and scattered solar flux, the computer analysis methods developed, and the results of the research, presented as both graphical and tabular data, are discussed