Numerical Relativity

La primera detección directa de ondas gravitacionales, obtenida recientemente en los detectores LIGO, abrió una nueva ventana al Universo. Adicionalmente, dado el rol que juega la relatividad numérica en la elaboración de catálogos de perfiles de ondas, este hallazgo propicia un empuje importante al modelado computacional de la radiación gravitacional. En este sentido, teniendo presente la importancia de simular sistemas aislados en esta área, recientemente ha habido un renovado interés en resolver numéricamente el problema de valores iniciales hiperboloidal para las ecuaciones de campo de Einstein, en el que la frontera exterior de la malla numérica se ubica en el infinito nulo futuro (scri+). En este trabajo implementamos numéricamente el enfoque tetradial BSB presentado en [J.M. Bardeen, O. Sarbach y L.T. Buchman, Phys. Rev. D 83, 104045 (2011)], para el caso de un campo escalar autogravitante, minimamente acoplado, esféricamente simétrico. Debido a la dificultad de esta tarea, introduciremos muchos de los ingredientes que necesitamos con tres pruebas numéricas previas. Partimos resolviendo la ecuación de onda en 1+1 dimensiones, luego resolvemos esta ecuación en el contexto de la relatividad espacial sobre un espacio-tiempo de Minkowski, para posteriormente resolver la ecuación de onda esféricamente simétrica de un campo escalar no masivo sobre un fondo de Schwarzschild. En las dos últimas pruebas implementamos métodos conformes, utilizando foliaciones en curvas (o bien hipersuperficies) tipo espacio, de curvatura extrínseca media constante (CMC) positiva que intersectan scri+, junto con compactificaciones que nos permiten mapear nuestro espacio-tiempo infinito a una variedad finita. Únicamente despues de realizar estas pruebas, es que nos volcamos al objetivo principal de este trabajo. Estudiaremos en detalle el enfoque BSB, para el caso general sin simetrías, y luego reduciremos el escenario a simetría esférica y trabajaremos en la implementación numérica incluyendo el ya mencionado campo escalar autogravitante. En particular, el sistema de evolución se reduce a un sistema de ecuaciones simétrico-hiperbólico de primer orden, regular, para el campo escalar conformemente reescalado, el cual se acopla a un conjunto de constricciones elípticas singulares para los coeficientes métricos. Aquí mostraremos como resolver este sistema, basándonos en aproximaciones de diferencias finitas, obteniendo evoluciones numéricas estables para configuraciones iniciales de agujeros negros rodeados por un cascarón esférico de campo escalar, resultando que una parte de este último se dispersa hacia scri+ y la otra parte es acretada por el agujero negro. Como una prueba no trivial, estudiamos el decaimiento de cola del campo escalar a lo largo de diferentes líneas de mundo: una situada a lo largo del horizonte (aparente), otra correspondiente a un observador tipo tiempo a un radio finito fuera del horizonte, y una última a lo largo de scri+. Nuestros resultados coinciden con la ley usual de decaimientos polinomiales predicha por la teoría linealizada, así como por trabajos previos.

We consider the Universe deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which perturb the background Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the most appropriate to describe the dynamics of the inhomogeneities which is defined, on the one hand, by gravitational potentials of inhomogeneities and, on the other hand, by the cosmological expansion of the Universe. In this paper, we present additional arguments in favor of this approach. First, we estimate the size of the cell of uniformity. With the help of the standard methods of statistical physics and for the galaxies of the type of the Milky Way and Andromeda, we get that it is of the order of 190 Mpc which is rather close to observations. Then, we show that the nonrelativistic approximation (with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the $\Lambda$CDM model, justify the main equations. Moreover, we demonstrate that radiation can be naturally incorporated into our scheme. This emphasizes the viability of our approach. This approach gives a possibility to analyze different cosmological models and compare them with the observable Universe. For example, we indicate some problematic aspects of the spatially flat models. Such models require a rather specific distribution of the inhomogeneities to get a finite potential at any points outside gravitating masses. We also criticize the application of the Schwarzschild-de Sitter solution to the description of the motion of test bodies on the cosmological background.

The isolated horizon formalism recently introduced by Ashtekar et al. aims at providing a quasi-local concept of a black hole in equilibrium in an otherwise possibly dynamical spacetime. In this formalism, a hierarchy of geometrical structures is constructed on a null hypersurface. On the other side, the 3+13+1 formulation of general relativity provides a powerful setting for studying the spacetime dynamics, in particular gravitational radiation from black hole systems. Here we revisit the kinematics and dynamics of null hypersurfaces by making use of some 3+13+1 slicing of spacetime. In particular, the additional structures induced on null hypersurfaces by the 3+13+1 slicing permit a natural extension to the full spacetime of geometrical quantities defined on the null hypersurface. This four-dimensional point of view facilitates the link between the null and spatial geometries. We proceed by reformulating the isolated horizon structure in this framework. We also reformulate previous works, such as Damour's black hole mechanics, and make the link with a previous 3+13+1 approach of black hole horizon, namely the membrane paradigm  . We explicit all geometrical objects in terms of 3+13+1 quantities, putting a special emphasis on the conformal 3+13+1 formulation. This is in particular relevant for the initial data problem of black hole spacetimes for numerical relativity. Illustrative examples are provided by considering various slicings of Schwarzschild and Kerr spacetimes.

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have bee...

We developed a new method for time-domain signal processing based on deep (dilated) convolutional neural networks which can rapidly identify and extract signals much weaker than the background noise. We applied this method for gravitational wave analysis and demonstrated that it significantly outperforms existing matched-filtering and conventional machine learning techniques and also extends the range of gravitational waves that can be detected by advanced LIGO, allowing real-time processing of raw big data with minimal resources. This initiates a new paradigm for research which uses massively-parallel simulations to train artificial intelligence algorithms that exploit emerging hardware architectures such as deep-learning-optimized GPUs. This approach provides a natural framework to enable coincident detection campaigns of gravitational waves sources and their electromagnetic counterparts.

We perform general relativistic, magnetohydrodynamic (GRMHD) simulations of merging binary neutron stars incorporating neutrino transport and magnetic fields. Our new radiative transport module for neutrinos adopts a general relativistic, truncated-moment (M1) formalism. The binaries consist of two identical, irrotational stars modeled by the SLy nuclear equation of state (EOS). They are initially in quasicircular orbit and threaded with a poloidal magnetic field that extends from the stellar interior into the exterior, as in typical pulsars. We insert neutrino processes shortly after the merger and focus on the role of neutrinos in launching a jet following the collapse of the hypermassive neutron star (HMNS) remnant to a spinning black hole (BH). We treat two microphysical versions: one (a "warm-up") evolving a single neutrino species and considering only charged-current processes, and the other evolving three species (νe,νe, νx) and related processes. We trace the evolution until the system reaches a quasiequilibrium state after BH formation. We find that the BH + disk remnant eventually launches an incipient jet. The electromagnetic Poynting luminosity is ∼ 10 53 erg s −1 , consistent with that of typical short gamma-ray bursts (sGRBs). The effect of neutrino cooling shortens the lifetime of the HMNS, and lowers the amplitude of the major peak of the gravitational wave (GW) power spectrum somewhat. After BH formation, neutrinos help clear out the matter near the BH poles, resulting in lower baryon-loaded surrounding debris. The neutrino luminosity resides in the range ∼ 10 52−53 erg s −1 once quasiequilibrium is achieved. Comparing with the neutrino-free models, we observe that the inclusion of neutrinos yields similar ejecta masses and is inefficient in carrying off additional angular momentum.

Black hole-neutron star mergers resulting in the disruption of the neutron star and the formation of an accretion disk and/or the ejection of unbound material are prime candidates for the joint detection of gravitational-wave and electromagnetic signals when the next generation of gravitational-wave detectors comes online. However, the disruption of the neutron star and the properties of the post-merger remnant are very sensitive to the parameters of the binary. In this paper, we study the impact of the radius of the neutron star and the alignment of the black hole spin for systems within the range of mass ratio currently deemed most likely for field binaries (M_BH ~ 7 M_NS) and for black hole spins large enough for the neutron star to disrupt (J/M^2=0.9). We find that: (i) In this regime, the merger is particularly sensitive to the radius of the neutron star, with remnant masses varying from 0.3M_NS to 0.1M_NS for changes of only 2 km in the NS radius; (ii) 0.01-0.05M_sun of unbound material can be ejected with kinetic energy >10^51 ergs, a significant increase compared to low mass ratio, low spin binaries. This ejecta could power detectable optical and radio afterglows. (iii) Only a small fraction (<3%) of the Advanced LIGO events in this parameter range have gravitational-wave signals which could offer constraints on the equation of state of the neutron star. (iv) A misaligned black hole spin works against disk formation, with less neutron star material remaining outside of the black hole after merger, and a larger fraction of that material remaining in the tidal tail instead of the forming accretion disk. (v) Large kicks (v>300 km/s) can be given to the final black hole as a result of a precessing BHNS merger, when the disruption of the neutron star occurs just outside or within the innermost stable spherical orbit.

Collapsing supermassive stars (SMSs) with masses M 10 4−6 M have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed general rel-ativistic magnetohydrodynamic (GRMHD) simulations of marginally stable Γ = 4/3 polytropes uniformly rotating at the mass-shedding limit and endowed initially with a dynamically unimportant dipole magnetic field to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and reliably model SMSs with M 10 6 M. We found that around 90% of the initial stellar mass forms a spinning black hole (BH) remnant surrounded by a massive, hot, magnetized torus, which eventually launches a magnetically-driven jet. SMSs could be therefore sources of ultra-long gamma-ray bursts (ULGRBs). Here we perform GRMHD simulations of Γ 4/3, polytropes to account for the perturbative role of gas pressure in SMSs with M 10 6 M. We also consider different initial stellar rotation profiles. The stars are initially seeded with a dynamically weak dipole magnetic field that is either confined to the stellar interior or extended from its interior into the stellar exterior. We calculate the gravitational wave burst signal for the different cases. We find that the mass of the black hole remnant is 90%−99% of the initial stellar mass, depending sharply on Γ−4/3 as well as on the initial stellar rotation profile. After t ∼ 250 − 550M ≈ 1 − 2 × 10 3 (M/10 6 M)s following the appearance of the BH horizon, an incipient jet is launched and it lasts for ∼ 10 4 − 10 5 (M/10 6 M)s, consistent with the duration of long gamma-ray bursts. Our numerical results suggest that the Blandford-Znajek mechanism powers the incipient jet. They are also in rough agreement with our recently proposed universal model that estimates accretion rates and electromagnetic (Poynting) luminosities that characterize magnetized BH-disk remnant systems that launch a jet. This model helps explain why the outgoing electromagnetic luminosities computed for vastly different BH-disk formation scenarios all reside within a narrow range (∼ 10 52±1 erg s −1), roughly independent of M .

In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach, the large scalaron mass approximation and the quasi-static approximation, getting explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function $f(R)$ and the scale factor $a$. Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of nonlinearity. Our investigation is valid for functions $f(R)$ which have stable de Sitter points in future with respect to the present time, that is typical for the most popular $f(R)$ models.

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

We present the first numerical simulations of an initially nonspinning black-hole binary with mass ratio as large as 10∶1 in full general relativity. The binary completes approximately three orbits prior to merger and radiates (0.415±0.017)% of the total energy and (12.48±0.62)% of the initial angular momentum in the form of gravitational waves. The single black hole resulting from the merger acquires a kick of (66.7±3.3)km/s relative to the original center of mass frame. The resulting gravitational waveforms are used to validate existing formulas for the recoil, final spin, and radiated energy over a wider range of the symmetric mass ratio parameter η=M1M2/(M1+M2)2 than previously possible. The contributions of ℓ>2 multipoles are found to visibly influence the gravitational wave signal obtained at fixed inclination angles.

White dwarf-neutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarf-neutron star (WDNS) binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass transfer (UMT), which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to estimate the number of LISA-resolved galactic binaries that will undergo either SMT or UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary differential equations and compute the corresponding gravitational waveforms. Finally, we discuss in general terms the possible fate of binaries that undergo UMT and construct approximate Newtonian equilibrium configurations of merged WDNS remnants. We use these configurations to assess plausible outcomes of our future, fully relativistic simulations of these systems. If sufficient WD debris lands on the NS, the remnant may collapse, whereby the gravitational waves from the inspiral, merger, and collapse phases will sweep from LISA through LIGO frequency bands. If the debris forms a disk about the NS, it may fragment and form planets.

Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a variety of systems self-similar solutions can describe asymptotic or intermediate behaviour of more general solutions in an approach to singularities. The typical example is the convergence to an attractor self-similar solution in gravitational collapse. This is closely related to the cosmic censorship violation in the spherically symmetric collapse of a perfect fluid. The self-similar solution also plays an important role in critical phenomena in gravitational collapse. The critical phenomena are understood as the intermediate behaviour around a critical self-similar solution. We see that the convergence and critical phenomena are understood in a unified manner in terms of attractors of codimension zero and one, respectively, in renormalisation group flow.

The present work shows how black hole information, such as mass and angular momentum, can be extracted via a new theoretical and computational analysis of the hole’s so called ringdown radiation, which is a gravitational wave emitted by a freely oscillating black hole.

This analysis fits within the broader field of numerical relativity whose treatment requires fast and robust computational algorithms. A new spectral algorithm is presented in this work that solves the spin weight spheroidal equation, describing angular perturbations of a black hole. We then use it together with Leaver’s continued fraction method to calculate quasinormal modes (QNM) of a Kerr black hole for multipole number l = 2 through 12 and first 8 overtones with  \epsilon= 10^(−12) accuracy.

The computed QNM spectrum is then used to represent the ringdown signal of a black hole, which is a signature radiation that corresponds to the hole’s parameters. According to the no-hair theorem these parameters are limited to the mass, angular momentum and charge. We assume the ringing black hole is electrically neutral so only the information about its mass and angular momentum is present in the ringdown signal. The multimode nonlinear fitting formalism, that we developed, allows us to extract that information from the black hole.

Assessing the quality of groundwater is important to ensure sustainable safe use of these resources. However, describing the overall water quality condition is difficult due to the spatial variability of multiple contaminants and the wide range of indicators (chemical, physical and biological) that could be measured. This contribution proposes a GIS-based groundwater quality index (GQI) which synthesizes different available water quality data (e.g., Cl−, Na+, Ca2+) by indexing them numerically relative to the World Health Organization (WHO) standards. Also, introduces an objective procedure to select the optimum parameters to compute the GQI, incorporates the aspect of temporal variation to address the degree of water use sustainability and tests the sensitivity of the proposed model. The GQI indicated that the groundwater quality in the Nasuno basin, Tochigi Prefecture, Japan, is generally high (GQI V, 15–30%) compared to the middle part (V,