Local characteristic algorithms for relativistic hydrodynamics

Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first applied in Newtonian hydrodynamics, provides a robust methodology to obtain stable and accurate solutions even in the presence of discontinuities. The knowledge of the wave structure of the above system is essential in the construction of the so-called linearized Riemann solvers, a class of numerical schemes specifically designed to solve nonlinear hyperbolic systems of conservation laws. In the last part of the review some astrophysical applications of such schemes, using the coupled system of the (characteristic) Einstein and hydrodynamic equations, are also briefly presented.Comment: 20 pages, 4 figures, To appear in the proceedings of the workshop "The conformal structure of space-time", J. Frauendiener, H. Friedrich, eds, Springer Lecture Notes in Physic

Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Kerr black hole

In our program of studying numerically the so-called Bondi-Hoyle accretion in the fully relativistic regime, we present here first results concerning the evolution of matter accreting supersonically onto a rotating (Kerr) black hole. These computations generalize previous results where the non-rotating (Schwarzschild) case was extensively considered. We parametrize our initial data by the asymptotic conditions for the fluid and explore the dependence of the solution on the angular momentum of the black hole. Towards quantifying the robustness of our numerical results, we use two different geometrical foliations of the black hole spacetime, the standard form of the Kerr metric in Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of coordinate singularities at the black hole horizon. We demonstrate some important advantages of using such horizon adapted coordinate systems. Our numerical study indicates that regardless of the value of the black hole spin the final accretion pattern is always stable, leading to constant accretion rates of mass and momentum. The flow is characterized by a strong tail shock, which, unlike the Schwarzschild case, is increasingly wrapped around the central black hole as the hole angular momentum increases. The rotation induced asymmetry in the pressure field implies that besides the well known drag, the black hole will experience also a lift normal to the flow direction. This situation exhibits some analogies with the Magnus effect of classical fluid dynamics.Comment: 33 pages, 20 figures, submited to MNRA

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

SUSY-breaking Soft Terms in a MSSM Magnetized D7-brane Model

We compute the SUSY-breaking soft terms in a magnetized D7-brane model with MSSM-like spectrum, under the general assumption of non-vanishing auxiliary fields of the dilaton and Kahler moduli. As a particular scenario we discuss SUSY breaking triggered by ISD or IASD 3-form fluxes.Comment: Latex, 27 pages, v2: added reference

The runaway instability of thick discs around black holes. I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical timescale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole ($2.5 \mathrm{M_\odot}$) and a large range of mass fluxes (\dot{m} \ga 10^{-3} \mathrm{M_{\odot}/s}). The implications of our results in the context of gamma-ray bursts are briefly discussed.Comment: 20 pages, 16 figures, to appear in MNRA

Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Schwarzschild black hole

We present the results of an exhaustive numerical study of fully relativistic non-axisymmetric Bondi-Hoyle accretion onto a moving Schwarzschild black hole. We have solved the equations of general relativistic hydrodynamics with a high-resolution shock-capturing numerical scheme based on a linearized Riemann solver. The numerical code was previously used to study axisymmetric flow configurations past a Schwarzschild hole. We have analyzed and discussed the flow morphology for a sample of asymptotically high Mach number models. The results of this work reveal that initially asymptotic uniform flows always accrete onto the hole in a stationary way which closely resembles the previous axisymmetric patterns. This is in contrast with some Newtonian numerical studies where violent flip-flop instabilities were found. As discussed in the text, the reason can be found in the initial conditions used in the relativistic regime, as they can not exactly duplicate the previous Newtonian setups where the instability appeared. The dependence of the final solution with the inner boundary condition as well as with the grid resolution has also been studied. Finally, we have computed the accretion rates of mass and linear and angular momentum.Comment: 21 pages, 13 figures, Latex, MNRAS (in press

Dynamics of thick discs around Schwarzschild-de Sitter black holes

We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting onto the black hole. To assess the impact of this outflow on the development of the instability we have performed time-dependent and axisymmetric hydrodynamical simulations of equilibrium initial configurations in a sequence of background spacetimes of Schwarzschild-de Sitter black holes with increasing masses. The simulations have been performed with an unrealistic value for the cosmological constant which, however, yields sufficiently small discs to be resolved accurately on numerical grids and thus provides a first qualitative picture of the dynamics. The calculations, carried out for a wide range of initial conditions, show that the mass-loss from the outer cusp can have a considerable impact on the instability, with the latter being rapidly suppressed if the outflow is large enough.Comment: 12 pages; A&A, in pres