A Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity

We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible to describe a black hole component by the puncture ansatz as well as through an excision technique. First examples are given for binary black hole excision data that fulfill the requirements of the quasi-stationary framework, which combines the Conformal Thin Sandwich formulation of the constraint equations with the Isolated Horizon conditions for black holes in quasi-equilibrium. These numerical solutions were obtained to extremely high accuracy with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large mass ratios of the binary components

How does militant violence diffuse in regions? Regional conflict systems in international relations and peace and conflict studies

Regional conflict systems are characterised by their complexity of actors, causes, structural conditions and dynamics. Such complexity poses difficulties to those looking to undertake scientific analysis of the regional dynamics of violence. It is still quite unclear how militant violence diffuses in regions and under which conditions a regional conflict system can emerge. This review of existing approaches to regional conflict dynamics in international studies and peace and conflict studies focuses on how the regional conflict dynamics and the causal mechanisms behind the development of regional conflict systems are dealt with, considering process dynamics in space and time as well as in the interactions between possible causal factors. The primary gaps in existing research are identified and possible new research directions sketched out.Regional conflict systems are characterised by their complexity of actors, causes, structural conditions and dynamics. Such complexity, however, poses difficulties to those looking to undertake scientific analysis of these processes. In the present paper existing approaches to regional conflict dynamics in international studies and peace and conflict studies are reviewed. Of particular interest is the question how these approaches dealt with regional violence in areas with limited or no statehood as this is one of the striking conditions for the emergence and diffusion of regional conflict systems. Starting from this question, the main research gaps that exist in the current literature on regional conflicts will be detected. Furthermore, new research directions will be pointed out

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.

A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.Comment: Contribution to the "Encuentros Relativistas Espanoles - Spanish Relativity Meeting ERE07" Proceedings, Tenerife, Spain (September 2007

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum J and charge Q of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation (8\pi J)2+(4\pi Q2)2=A+ A-, where A+ and A- denote the areas of event and Cauchy horizon respectively

On the multipole moments of a rigidly rotating fluid body

Based on numerical simulations and analytical calculations we formulate a new conjecture concerning the multipole moments of a rigidly rotating fluid body in equilibrium. The conjecture implies that the exterior region of such a fluid is not described by the Kerr metric.Comment: 5 pages, 4 figures, to appear in Annalen der Physi

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

The Parametric Transition of Strange Matter Rings to a Black Hole

It is shown numerically that strange matter rings permit a continuous transition to the extreme Kerr black hole. The multipoles as defined by Geroch and Hansen are studied and suggest a universal behaviour for bodies approaching the extreme Kerr solution parametrically. The appearance of a `throat region', a distinctive feature of the extreme Kerr spacetime, is observed. With regard to stability, we verify for a large class of rings, that a particle sitting on the surface of the ring never has enough energy to escape to infinity along a geodesic.Comment: 16 pages, 11 figures, v3: minor changes so as to coincide with published versio