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

Epidemiologische Untersuchungen zur Eimeria-Infektion bei Kälbern und Jungrindern in Schleswig-Holstein

Ziel dieser epidemiologischen Studie war es, das Vorkommen und das Artenspektrum von Eimeria spp. sowie den Infektionsverlauf in zwei konventionell geführten landwirtschaftlichen Betrieben in Schleswig-Holstein unter Feldbedingungen zu untersuchen und eine Behandlungsstrategie abzuleiten

Das Verschwinden der Hörigkeit und die Wandlungen der Grundherrschaft in England und Italien : Bauernbefreiung und Grundentlastung in Deutschland und Russland vol. 6

- Inhalt #13- Das Verschwinden der Hörigkeit in England #15- Der Abschluss der Auflösung der englischen Gutswirtschaft im XVI #65- Der Wendepunkt in der Geschichte des Grundbesitzes in England #146- Wandlungen der Grundherrschaft die Gemeinnutzung in Italien #223- Die Geschichte der Patriziate des Tessin und der Partecipanzen der Emilia und der Romagna #305- Der Einfluss der Lehren der Volkswirtschaft #364- Kurze Uebersicht in Deutschland #395- Kurze Uebersicht der Bauernbefreiung in Russland #42

A Roche Model for Uniformly Rotating Rings

A Roche model for describing uniformly rotating rings is presented and the results are compared with numerical solutions to the full problem for polytropic rings. In the thin ring limit, the surfaces of constant pressure including the surface of the ring itself are given in analytic terms, even in the mass-shedding case.Comment: 6 pages, 4 figures, v2: minor correction

Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity

Using a multi domain spectral method, we investigate systematically the general-relativistic model for axisymmetric uniformly rotating, homogeneous fluid bodies generalizing the analytically known Maclaurin and Schwarzschild solutions. Apart from the curves associated with these solutions and a further curve of configurations that rotate at the mass shedding limit, two more curves are found to border the corresponding two parameter set of solutions. One of them is a Newtonian lens shaped sequence bifurcating from the Maclaurin spheroid sequence, while the other one corresponds to highly relativistic bodies with an infinite central pressure. The properties of the configuration for which both the gravitational and the baryonic masses, moreover angular velocity, angular momentum as well as polar red shift obtain their maximal values are discussed in detail. In particular, by comparison with the static Schwarzschild solution, we obtain an increase of 34.25% in the gravitational mass. Moreover, we provide exemplarily a discussion of angular velocity and gravitational mass on the entire solution class.Comment: 4 pages, 4 figures, 1 table, submitted to A&A, corrected eq. for W, W' in 3.

Black Holes Surrounded by Uniformly Rotating Rings

Highly accurate numerical solutions to the problem of Black Holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some detail. Related Newtonian problems are described and numerical results provided, which show that configurations can reach an inner mass-shedding limit as the mass of the central object increases. Exemplary results for the full relativistic problem for rings of constant density are given and the deformation of the event horizon due to the presence of the ring is demonstrated. Finally, we provide an example of a system for which the angular momentum of the central Black Hole divided by the square of its mass exceeds one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected, corresponds to version in PR

Uniformly Rotating Homogeneous Rings in post-Newtonian Gravity

In this paper uniformly rotating relativistic rings are investigated analytically utilizing two different approximations simultaneously: (1) an expansion about the thin ring limit (the cross-section is small compared with the size of the whole ring) (2) post-Newtonian expansions. The analytic results for rings are compared with numerical solutions.Comment: 12 pages, 7 figures, v1: 2 tables added, agrees with published versio

Stationary motion of a self gravitating toroidal incompressible liquid layer

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stratum we show the existence of stationary motions during which the stratum is approximatly a round torus (with radii r, R and R>>r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R that connects the centers of the cross sections of the torus

Highly accurate calculation of rotating neutron stars

A new spectral code for constructing general-relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with those obtained by several previous codes. Moreover, representative relativistic examples corresponding to highly flattened rotating bodies are given.Comment: 4 pages, submitted to Astronomy & Astrophysic

Equilibrium configurations of fluids and their stability in higher dimensions

We study equilibrium shapes, stability and possible bifurcation diagrams of fluids in higher dimensions, held together by either surface tension or self-gravity. We consider the equilibrium shape and stability problem of self-gravitating spheroids, establishing the formalism to generalize the MacLaurin sequence to higher dimensions. We show that such simple models, of interest on their own, also provide accurate descriptions of their general relativistic relatives with event horizons. The examples worked out here hint at some model-independent dynamics, and thus at some universality: smooth objects seem always to be well described by both ``replicas'' (either self-gravity or surface tension). As an example, we exhibit an instability afflicting self-gravitating (Newtonian) fluid cylinders. This instability is the exact analogue, within Newtonian gravity, of the Gregory-Laflamme instability in general relativity. Another example considered is a self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical and Quantum Gravity. v2: Minor corrections and references adde