Accurate evolutions of inspiralling and magnetized neutron-stars: equal-mass binaries

By performing new, long and numerically accurate general-relativistic simulations of magnetized, equal-mass neutron-star binaries, we investigate the role that realistic magnetic fields may have in the evolution of these systems. In particular, we study the evolution of the magnetic fields and show that they can influence the survival of the hypermassive-neutron star produced at the merger by accelerating its collapse to a black hole. We also provide evidence that even if purely poloidal initially, the magnetic fields produced in the tori surrounding the black hole have toroidal and poloidal components of equivalent strength. When estimating the possibility that magnetic fields could have an impact on the gravitational-wave signals emitted by these systems either during the inspiral or after the merger we conclude that for realistic magnetic-field strengths B<~1e12 G such effects could be detected, but only marginally, by detectors such as advanced LIGO or advanced Virgo. However, magnetically induced modifications could become detectable in the case of small-mass binaries and with the development of gravitational-wave detectors, such as the Einstein Telescope, with much higher sensitivities at frequencies larger than ~2 kHz.Comment: 18 pages, 10 figures. Added two new figures (figures 1 and 7). Small modifications to the text to match the version published on Phys. Rev.

On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations

Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived by addition of combinations of the constraints and their derivatives to the right-hand-side of the ADM evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic - second-order parabolic. The second formulation is a parabolization of the Kidder, Scheel, Teukolsky formulation and is a manifestly mixed strongly hyperbolic - second-order parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.Comment: 19 pages, two column, references added, two proofs of well-posedness added, content changed to agree with submitted version to PR

Concadia: Towards Image-Based Text Generation with a Purpose

Current deep learning models often achieve excellent results on benchmark image-to-text datasets but fail to generate texts that are useful in practice. We argue that to close this gap, it is vital to distinguish descriptions from captions based on their distinct communicative roles. Descriptions focus on visual features and are meant to replace an image (often to increase accessibility), whereas captions appear alongside an image to supply additional information. To motivate this distinction and help people put it into practice, we introduce the publicly available Wikipedia-based dataset Concadia consisting of 96,918 images with corresponding English-language descriptions, captions, and surrounding context. Using insights from Concadia, models trained on it, and a preregistered human-subjects experiment with human- and model-generated texts, we characterize the commonalities and differences between descriptions and captions. In addition, we show that, for generating both descriptions and captions, it is useful to augment image-to-text models with representations of the textual context in which the image appeared.Comment: Proceedings of EMNLP 202

Gowdy waves as a test-bed for constraint-preserving boundary conditions

Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting 200

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ

3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.Comment: 21 pages. To appear in PR

Numerical evolutions of a black hole-neutron star system in full General Relativity: I. Head-on collision

We present the first simulations in full General Relativity of the head-on collision between a neutron star and a black hole of comparable mass. These simulations are performed through the solution of the Einstein equations combined with an accurate solution of the relativistic hydrodynamics equations via high-resolution shock-capturing techniques. The initial data is obtained by following the York-Lichnerowicz conformal decomposition with the assumption of time symmetry. Unlike other relativistic studies of such systems, no limitation is set for the mass ratio between the black hole and the neutron star, nor on the position of the black hole, whose apparent horizon is entirely contained within the computational domain. The latter extends over ~400M and is covered with six levels of fixed mesh refinement. Concentrating on a prototypical binary system with mass ratio ~6, we find that although a tidal deformation is evident the neutron star is accreted promptly and entirely into the black hole. While the collision is completed before ~300M, the evolution is carried over up to ~1700M, thus providing time for the extraction of the gravitational-wave signal produced and allowing for a first estimate of the radiative efficiency of processes of this type.Comment: 16 pages, 12 figure