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

Hyperfine splittings in the bbˉb\bar{b} system

Recent measurements of the $\eta_b(1S)$, the ground state of the $b\bar{b}$ system, show the splitting between it and the \Up(1S) to be 69.5$\pm$3.2 MeV, considerably larger than lattice QCD and potential model predictions, including recent calculations published by us. The models are unable to incorporate such a large hyperfine splitting within the context of a consistent description of the energy spectrum and decays. We demonstrate that in our model, which incorporates a relativistic kinetic energy term, a linear confining term including its scalar-exchange relativistic corrections, and the complete one-loop QCD short distance potential, such a consistent description, including the measured hyperfine splitting, can be obtained by not softening the delta function terms in the hyperfine potential. We calculate the hyperfine splitting to be 67.5 MeV.Comment: 5 pages, 3 tables, text revision

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

Relativistic Dyson Rings and Their Black Hole Limit

In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references added, accepted for publication in Astrophys. J. Let

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

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

Dynamics of charged fluids and 1/L perturbation expansions

Some features of the calculation of fluid dynamo systems in magnetohydrodynamics are studied. In the coupled set of the ordinary linear differential equations for the spherically symmetric $\alpha^2-$dynamos, the problem represented by the presence of the mixed (Robin) boundary conditions is addressed and a new treatment for it is proposed. The perturbation formalism of large$-\ell$ expansions is shown applicable and its main technical steps are outlined.Comment: 16 p

Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions

The monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for gravity coupled bosonic dynamics in string gravity and supergravity in four and higher dimensions. For different types of fields in space-times of $D\ge 4$ dimensions with $d=D-2$ commuting isometries -- stationary fields with spatial symmetries, interacting waves or partially inhomogeneous cosmological models, the string gravity equations govern the dynamics of interacting gravitational, dilaton, antisymmetric tensor and any number $n\ge 0$ of Abelian vector gauge fields (all depending only on two coordinates). The equivalent spectral problem constructed earlier allows to parameterize the infinite-dimensional space of local solutions of these equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic $d\times d$- and $d\times n$- matrix functions ${\mathbf{u}_\pm(w), \mathbf{v}_\pm(w)}$ of a spectral parameter $w$ which constitute a complete set of monodromy data for normalized fundamental solution of this spectral problem. The "direct" and "inverse" problems of such monodromy transform --- calculating the monodromy data for any local solution and constructing the field configurations for any chosen monodromy data always admit unique solutions. We construct the linear singular integral equations which solve the inverse problem. For any \emph{rational} and \emph{analytically matched} (i.e. $\mathbf{u}_+(w)\equiv\mathbf{u}_-(w)$ and $\mathbf{v}_+(w)\equiv\mathbf{v}_-(w)$) monodromy data the solution for string gravity equations can be found explicitly. Simple reductions of the space of monodromy data leads to the similar constructions for solving of other integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or vacuum gravity in $D\ge 4$ dimensions.Comment: RevTex 7 pages, 1 figur

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure