Making use of geometrical invariants in black hole collisions

We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the {\sl speciality index} ${\cal S}$. In the context of black hole perturbations $\cal S$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes ${\cal S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.Comment: 4 pages, 3 eps figures, Revte

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

Constraint Damping in First-Order Evolution Systems for Numerical Relativity

A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel and Teukolsky (KST). The auxiliary fields, introduced to make the KST system first-order, are given modified evolution equations designed to drive constraint violations toward zero. The algebraic structure of the new system is investigated, showing that the modifications preserve the hyperbolicity of the fundamental and constraint evolution equations. The evolution of the constraints for pertubations of flat spacetime is completely analyzed, and all finite-wavelength constraint modes are shown to decay exponentially when certain adjustable parameters satisfy appropriate inequalities. Numerical simulations of a single Schwarzschild black hole are presented, demonstrating the effectiveness of the new constraint-damping modifications.Comment: 11 pages, 5 figure

"Are Black Holes in Brans-Dicke Theory precisely the same as in General Relativity?"

We study a three-parameters family of solutions of the Brans-Dicke field equations. They are static and spherically symmetric. We find the range of parameters for which this solution represents a black hole different from the Schwarzschild one. We find a subfamily of solutions which agrees with experiments and observations in the solar system. We discuss some astrophysical applications and the consequences on the "no hair" theorems for black holes.Comment: 13pages, Plain Te

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

Three-family oscillations using neutrinos from muon beams at very long baseline

The planned LBL experiments will be able to prove the hypothesis of flavor oscillation between muon and tau neutrinos. We explore the possibility of a second generation long baseline experiment at very long baseline, i.e. L in the range 5000-7000 km. This distance requires intense neutrino beams that could be available from very intense muon beams as those needed for $\mu$ colliders. Such baselines allow the study of neutrino oscillations with $E/L \approx 2\times 10^{-3} eV^2$ with neutrinos of energy $E_\nu \approx 10 GeV$, i.e. above tau threshold. Moreover, matter effects inside the Earth could lead to observable effects in $\nu_e \to \nu_\mu$ oscillations. These effects are interchanged between neutrinos and antineutrinos, and therefore they can be tested by comparing the oscillated spectra obtained running the storage ring with positive and negative muons.Comment: 14 pages, 4 figure

A medium baseline search for νμ→νe\nu_\mu\to\nu_e oscillations at a ν\nu beam from muon decays

The accurate knowledge of the $\bar\nu_e (\nu_\mu)$ beam produced in $\mu^-$ decays and the absence of $\nu_e (\bar\nu_\mu)$ contamination, make a future muon storage ring the ideal place to look for \numunue (\numubarnuebar) oscillations. Using a detector capable of electron and muon identification with charge discrimination (e.g., the presently running NOMAD experiment), good sensitivities to \numunue (\numubarnuebar) oscillations could be achieved. With the CERN-PS as a proton driver for a muon storage ring of the kind envisaged for a $\mu$-collider, the LSND claim would be confirmed or disproved in a few years of running.Comment: 10 pages, 4 figure