The Exact Solution of the Riemann Problem in Relativistic MHD

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an important test for those numerical codes solving the MHD equations in relativistic regimes.Comment: 36 pages, 13 figures. Minor changes to match published versio

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

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

General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars

We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed at assessing the modifications introduced by resistive effects on the dynamics of the binary after the merger and through to collapse, we have carried out a close comparison with an equivalent simulation performed within the traditional ideal magnetohydrodynamic approximation. We have found that there are many similarities between the two evolutions but also one important difference: the survival time of the hyper massive neutron star increases in a RMHD simulation. This difference is due to a less efficient magnetic-braking mechanism in the resistive regime, in which matter can move across magnetic-field lines, thus reducing the outward transport of angular momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried here have been performed at higher resolutions and with a different grid structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732, L6 (2011)], but confirm the formation of a low-density funnel with an ordered magnetic field produced by the black hole--torus system. In both regimes the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Reconnection processes or neutrino annihilation occurring in the funnel, none of which we model, could potentially increase the internal energy in the funnel and launch a relativistic outflow, which, however, is not produced in these simulations.Comment: 26 pages, 17 figures; animations available at http://www.southampton.ac.uk/~kd10g13/movies/index.shtm

Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes

The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity and in the geometric characterization of black hole horizons open new conceptual and technical avenues into the problem. We discuss here a research methodology in which spacetime dynamics is probed through the cross-correlation of geometric quantities constructed on the black hole horizon and on null infinity. These two hypersurfaces respond to evolving gravitational fields in the bulk, providing canonical "test screens" in a "scattering"-like perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial Value Problem approach to the construction of generic spacetimes and discuss the role and properties of dynamical trapping horizons as canonical inner "screens" in this context. We apply these ideas and techniques to the study of the recoil dynamics in post-merger binary black holes, an important issue in supermassive galactic black hole mergers.Comment: 16 pages, 5 figures, contribution to the proceedings volume of the Spanish Relativity Meeting ERE2011: "Towards new paradigms", Madrid, Spain, 29 Aug-2 Sep 201

Relativistic simulations of the phase-transition-induced collapse of neutron stars

An increase in the central density of a neutron star may trigger a phase transition from hadronic matter to deconfined quark matter in the core, causing it to collapse to a more compact hybrid-star configuration. We present a study of this, building on previous work by Lin et al. (2006). We follow them in considering a supersonic phase transition and using a simplified equation of state, but our calculations are general relativistic (using 2D simulations in the conformally flat approximation) as compared with their 3D Newtonian treatment. We also improved the treatment of the initial phase transformation, avoiding the introduction of artificial convection. As before, we find that the emitted gravitational-wave spectrum is dominated by the fundamental quasi-radial and quadrupolar pulsation modes but the strain amplitudes are much smaller than suggested previously, which is disappointing for the detection prospects. However, we see significantly smaller damping and observe a nonlinear mode resonance which substantially enhances the emission in some cases. We explain the damping mechanisms operating, giving a different view from the previous work. Finally, we discuss the detectability of the gravitational waves, showing that the signal-to-noise ratio for current or second generation interferometers could be high enough to detect such events in our Galaxy, although third generation detectors would be needed to observe them out to the Virgo cluster, which would be necessary for having a reasonable event rate.Comment: 28 pages, 27 figures. Minor changes to be consistent with published versio

Rossby-Haurwitz waves of a slowly and differentially rotating fluid shell

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves (the analogues of r waves on a thin-shell) in the presence of differential rotation. The results obtained indicate that the eigenvalue problem is never singular and that, at least for the case of a thin-shell, the analogues of r modes can be found for arbitrarily large degrees of differential rotation. This work clarifies the puzzling results obtained in calculations of differentially rotating axi-symmetric Newtonian stars.Comment: 8pages, 3figures. Submitted to CQ