0000000000061090
AUTHOR
José María Ibáñez
Spanish Relativity Meeting (ERE 2014): almost 100 years after Einstein's revolution
This volume presents the proceedings of the international scientific conference ''Spanish Relativity Meeting (ERE 2014): almost 100 years after Einstein's revolution''. The conference was devoted to discussing the current state-of-the-art of a wide variety of topics of research in the fields of Gravitation and General Relativity in the ''pre-centennial'' year of General Relativity. The name of the conference was chosen to highlight the importance of the upcoming one hundredth anniversary of Einstein's theory of General Relativity, officially established by the Internal Society on General Relativity and Gravitation in November 25th, 2015. In particular, the conference was organized along thr…
On the convexity of Relativistic Hydrodynamics
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\it Rev. Mod. Phys.} {\bf 61} 75). The classical limit is recovered.
Numerical Simulations of Relativistic Wind Accretion onto Black Holes Using Godunov-Type Methods
We have studied numerically the so-called Bondi-Hoyle (wind) accretion onto a rotating black hole in general relativity. We have used the Kerr-Schild form of the Kerr metric, free of coordinate singularities at the black hole horizon. The ‘test-fluid’ approximation has been adopted, assuming no dynamical evolution of the gravitational field. We have used a formulation of the relativistic hydrodynamic equations which casts them into a first-order hyperbolic system of conservation laws. Our studies were performed using a Godunov-type scheme based on Marquina’s flux-formula.
Total-variation methods for gravitational-wave denoising: Performance tests on Advanced LIGO data
We assess total-variation methods to denoise gravitational-wave signals in real noise conditions, by injecting numerical-relativity waveforms from core-collapse supernovae and binary black hole mergers in data from the first observing run of Advanced LIGO. This work is an extension of our previous investigation where only Gaussian noise was used. Since the quality of the results depends on the regularization parameter of the model, we perform an heuristic search for the value that produces the best results. We discuss various approaches for the selection of this parameter, either based on the optimal, mean, or multiple values, and compare the results of the denoising upon these choices. Mor…
Shock capturing methods in 1D numerical relativity
A numerical code is presented which uses modern shock capturing methods to evolve spherically symmetric perfect fluid space-times. Harmonic slicing is used to ensure singularity avoidance, which is crucial in strong field situations. Some tests are presented, including an application to the stellar collapse problem.
Anomalous dynamics triggered by a non-convex equation of state in relativistic flows
The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density ($n_0 \approx 0.16\,$fm$^{-3}$) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, whose parameters can be restricted heeding to causality and thermodynamic stability constraints. This EoS shall be regarded as a toy-model wi…
Numerical Relativistic Hydrodynamics
High Resolution Shock Capturing (HRSC) techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. I will show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. I will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. In the second part, I will illustra…
Denoising of gravitational wave signals via dictionary learning algorithms
Gravitational wave astronomy has become a reality after the historical detections accomplished during the first observing run of the two advanced LIGO detectors. In the following years, the number of detections is expected to increase significantly with the full commissioning of the advanced LIGO, advanced Virgo and KAGRA detectors. The development of sophisticated data analysis techniques to improve the opportunities of detection for low signal-to-noise-ratio events is, hence, a most crucial effort. In this paper, we present one such technique, dictionary-learning algorithms, which have been extensively developed in the last few years and successfully applied mostly in the context of image…
Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as…
Split Bregman Method for Gravitational Wave Denoising
This paper presents a progress report in our aim to develop a Total Variation algorithm for denoising of gravitational waves. These algorithms, are routinely employed in the context of image processing and they do not need any a priori information on the signals. We apply our method to two different types of numerically-simulated gravitational wave signals, namely burst produced from the core collapse of rotating stars and waveforms from binary black hole mergers, and present a preliminary assessment of its capabilities.
Gravitational waves in Fully Constrained Formulation in a dynamical spacetime with matter content
We analyze numerically the behaviour of the hyperbolic sector of the Fully Constrained Formulation (FCF) (Bonazzola et al. 2004). The numerical experiments allow us to be confident in the performances of the upgraded version of the CoCoNuT code (Dimmelmeier et al. 2005) by replacing the Conformally Flat Condition (CFC), an approximation of Einstein equations, by FCF. First gravitational waves in FCF in a dynamical spacetime with matter content will be shown.
On numerical relativistic hydrodynamics and barotropic equations of state
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly modified in the case of evolving barotropic flows. For a barotropic equation of state, a removable singularity appears in one of the eigenvectors. The singularity can be avoided by means of a simple renormalization which makes the system of eigenvectors well defined and complete. An alternative strategy for the particular case of barotropic flows is discussed.
Gravitational waves from the collapse and bounce of a stellar core in tensor-scalar gravity
Tensor-scalar theory of gravity allows the generation of gravitational waves from astrophysical sources, like Supernov\ae{}, even in the spherical case. That motivated us to study the collapse of a degenerate stellar core, within tensor-scalar gravity, leading to the formation of a neutron star through a bounce and the formation of a shock. We discuss in this paper the effects of the scalar field on the evolution of the system, as well as the appearance of strong non-perturbative effects of this scalar field (the so-called ``spontaneous scalarization''). As a main result, we describe the resulting gravitational monopolar radiation (form and amplitude) and discuss the possibility of its dete…
Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic system. We have carried out a preliminary analysis of the mathematical structure of that system, in particular focusing on the equations governing the evolution for the deviation of a conformal metric from a flat fiducial one. The choice of a Dirac's gauge for the spatial coordinates guarantees the mathematical characterization of that system as a (strongly) hyperbolic system of conservation laws. In the presence of boundaries, this characterization also depen…
Characteristic structure of the resistive relativistic magnetohydrodynamic equations
We present the analysis of the characteristic structure of the resistive (non-ideal) relativistic magnetohydrodynamics system of equations. This is a necessary step to develop high-resolution shock-capturing schemes that use the full characteristic information (Godunov-type methods), and it is convenient to establish proper boundary conditions.
Stability analysis of relativistic jets from collapsars and its implications on the short-term variability of gamma-ray bursts
We consider the transverse structure and stability properties of relativistic jets formed in the course of the collapse of a massive progenitor. Our numerical simulations show the presence of a strong shear in the bulk velocity of such jets. This shear can be responsible for a very rapid shear--driven instability that arises for any velocity profile. This conclusion has been confirmed both by numerical simulations and theoretical analysis. The instability leads to rapid fluctuations of the main hydrodynamical parameters (density, pressure, Lorentz factor, etc.). However, the perturbations of the density are effectively decoupled from those of the pressure because the beam of the jet is radi…
Neutron star collapse and gravitational waves with a non-convex equation of state
The thermodynamical properties of the equation of state (EoS) of high-density matter (above nuclear saturation density) and the possible existence of exotic states such as phase transitions from nuclear/hadronic matter into quark-gluon plasma, or the appearance of hyperons, may critically influence the stability and dynamics of compact relativistic stars. From a theoretical point of view, establishing the existence of those states requires the analysis of the `convexity' of the EoS. We show indications of the existence of regions in the dense-matter EoS where the thermodynamics may be non-convex as a result of a non-monotonic dependence of the sound speed with the rest-mass density. When th…
Numerical evolution of matter in dynamical axisymmetric black hole spacetimes
We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses the characteristic information of the general relativistic hydrodynamic equations to build up a linearized Riemann solver. The spacetime is evolved with an axisymmetric ADM code designed to evolve a wormhole in full general relativity. We discuss the numerical and algorithmic issues related to the effective coupling of the hydrodynamical and spacetime pieces of the code, as well as the numerical methods and gauge conditions we use to evolve such spacetime…
Dynamical spacetimes and gravitational radiation in a Fully Constrained Formulation
This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be confident in the performances of the upgraded version of CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation of the Einstein equations by the FCF.
Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation
The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability andconvergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of…
Total-variation-based methods for gravitational wave denoising
We describe new methods for denoising and detection of gravitational waves embedded in additive Gaussian noise. The methods are based on Total Variation denoising algorithms. These algorithms, which do not need any a priori information about the signals, have been originally developed and fully tested in the context of image processing. To illustrate the capabilities of our methods we apply them to two different types of numerically-simulated gravitational wave signals, namely bursts produced from the core collapse of rotating stars and waveforms from binary black hole mergers. We explore the parameter space of the methods to find the set of values best suited for denoising gravitational wa…
On the local existence of maximal slicings in spherically symmetric spacetimes
In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.
Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations
We present a new three-dimensional general relativistic hydrodynamics code which is intended for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. Contrary to the common approach followed in most existing three-dimensional numerical relativity codes which are based in Cartesian coordinates, in this code both the metric and the hydrodynamics equations are formulated and solved numerically using spherical polar coordinates. A distinctive feature of this new code is the combination of two types of accurate numerical schemes specifically designed to solve each system of equations. More precisely, the code uses spectra…
Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach
We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e. Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jac…
Stellar hydrodynamics with glaister's riemann solver: An approach to the stellar collapse
La resolution de Remann approximee de la solution des equations d'Euler de la dynamique des gaz 1 D, developpee par Glaister P. (1988, J. Comput. Phys., 74) est introduite dans un code hydrodynamique lagrangien et appliquee a l'effondrement stellaire a symetrie spherique
Jet stability and the generation of superluminal and stationary components
We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component, instead of being ejected from the core. Their oblique nature should also result in distinc…
Trapping Horizons as inner boundary conditions for black hole spacetimes
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
Maximal slicings in spherical symmetry: Local existence and construction
We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by product, we suggest some applications of our work in the task of calibrating Numerical Relativity complex codes, usually written in Cartesian coordinates.