Invited papers from the international meeting on 'New Frontiers in Numerical Relativity' (Albert Einstein Institute, Potsdam, Germany, 17-21 July 2006)

Traditionally, frontiers represent a treacherous terrain to venture into, where hidden obstacles are present and uncharted territories lie ahead. At the same time, frontiers are also a place where new perspectives can be appreciated and have often been the cradle of new and thriving developments. With this in mind and inspired by this spirit, the Numerical Relativity Group at the Albert Einstein Institute (AEI) organized a `New Frontiers in Numerical Relativity' meeting on 17–21 July 2006 at the AEI campus in Potsdam, Germany

Prediction of ductile fracture in anisotropic steels for pipeline applications

Large diameter steel pipelines for gas transportation may experience extreme overloads due to external actions such as soil sliding, faults movements, third part interactions. In these scenarios the material undergoes severe plastic strains which locally may reach the fracture limits. Due to the manufacturing process, the steels used in such applications have an anisotropic behavior both for plasticity and fracture. In this paper two steel grades have been characterized in view of anisotropic plastic fracture. Fracture tests have been planned to characterize the fracture behavior under different stress states and in different directions to define the anisotropic sensitivity. Finite element modelling, incorporating an anisotropic plasticity formulation, has been used to calculate the local fracture parameters in the specimens and to define the complete ductile fracture locus. An uncoupled damage evolution law has been finally used to evaluate the fracture limits on real pipelines failed in full scale laboratory tests. The strain to fracture prediction has been verified by local strain measurements on the fractured pipes. The model robustness has been also verified on global parameter predictions, such us the burst pressur

A Complete Statistical Analysis for the Quadrupole Amplitude in an Ellipsoidal Universe

A model of Universe with a small eccentricity due to the presence of a magnetic field at the decoupling time (i.e. an Ellipsoidal Universe) has been recently proposed for the solution of the low quadrupole anomaly of the angular power spectrum of cosmic microwave background anisotropies. We present a complete statistical analysis of that model showing that the probability of increasing of the amplitude of the quadrupole is larger than the probability of decreasing in the whole parameters' space.Comment: 5 pages, 3 figure

Dynamics of Ferromagnetic Walls: Gravitational Properties

We discuss a new mechanism which allows domain walls produced during the primordial electroweak phase transition. We show that the effective surface tension of these domain walls can be made vanishingly small due to a peculiar magnetic condensation induced by fermion zero modes localized on the wall. We find that in the perfect gas approximation the domain wall network behaves like a radiation gas. We consider the recent high-red shift supernova data and we find that the corresponding Hubble diagram is compatible with the presence in the Universe of a ideal gas of ferromagnetic domain walls. We show that our domain wall gas induces a completely negligible contribution to the large-scale anisotropy of the microwave background radiation.Comment: Replaced with revised version, accepted for publication in IJMP

Testing the Isotropy of the Universe with Type Ia Supernovae

We analyze the magnitude-redshift data of type Ia supernovae included in the Union and Union2 compilations in the framework of an anisotropic Bianchi type I cosmological model and in the presence of a dark energy fluid with anisotropic equation of state. We find that the amount of deviation from isotropy of the equation of state of dark energy, the skewness \delta, and the present level of anisotropy of the large-scale geometry of the Universe, the actual shear \Sigma_0, are constrained in the ranges -0.16 < \delta < 0.12 and -0.012 < \Sigma_0 < 0.012 (1\sigma C.L.) by Union2 data. Supernova data are then compatible with a standard isotropic universe (\delta = \Sigma_0 = 0), but a large level of anisotropy, both in the geometry of the Universe and in the equation of state of dark energy, is allowed.Comment: 12 pages, 7 figures, 2 tables. Union2 analysis added. New references added. To appear in Phys. Rev.

The importance of precession in modelling the direction of the final spin from a black-hole merger

The prediction of the spin of the black hole resulting from the merger of a generic black-hole binary system is of great importance to study the cosmological evolution of supermassive black holes. Several attempts have been recently made to model the spin via simple expressions exploiting the results of numerical-relativity simulations. Here, I first review the derivation of a formula, proposed in Barausse & Rezzolla, Apj 704 L40, which accurately predicts the final spin magnitude and direction when applied to binaries with separations of hundred or thousands of gravitational radii. This makes my formula particularly suitable for cosmological merger-trees and N-body simulations, which provide the spins and angular momentum of the two black holes when their separation is of thousands of gravitational radii. More importantly, I investigate the physical reason behind the good agreement between my formula and numerical relativity simulations, and nail it down to the fact that my formula takes into account the post-Newtonian precession of the spins and angular momentum in a consistent manner.Comment: 6 pages, 2 figures. Panel added to fig 2, discussion extended to comply with referee's comments. Version accepted for publication as proceeding of the 8th Amaldi International Conference on Gravitational Waves, NYC, 21-26 June 200

The Lazarus project: A pragmatic approach to binary black hole evolutions

We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary black hole system with the numerical simulation covering the essential non-linear interaction before the close limit becomes applicable for the late time dynamics. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and non-linear treatments near the interface. Once the numerically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar $\psi_4$ and its time derivative $\partial_t\psi_4$ with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black hole binary systems which we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and collected by Bernard Kelly

Lorentz Symmetry Violation and Galactic Magnetism

We analyze the generation of primordial magnetic fields during de Sitter inflation in a Lorentz-violating theory of Electrodynamics containing a Chern-Simons term which couples the photon to an external four-vector. We find that, for appropriate magnitude of the four-vector, the generated field is maximally helical and, through an inverse cascade caused by turbulence of primeval plasma, reaches at the time of protogalactic collapse an intensity and correlation length such as to directly explain galactic magnetism.Comment: 5 pages, minor revisions, version published in Phys. Lett.