Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

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

Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests

We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems such as spherical dust collapse, stability test of perturbed spherical stars, and preservation of (approximate) equilibrium states of rapidly rotating neutron star and/or corotating binary neutron stars. These test simulations confirm that simulations of coalescing binary neutron stars are feasible in a numerical relativity code. It is illustrated that using our numerical code, simulations of these problems, in particular those of corotating binary neutron stars, can be performed stably and fairly accurately for a couple of dynamical timescales. These numerical results indicate that our formulation for solving the Einstein field equation and hydrodynamic equations are robust and make it possible to perform a realistic simulation of coalescing binary neutron stars for a long time from the innermost circular orbit up to formation of a black hole or neutron star.Comment: 36 pages, to be published in PRD 15, erase unnecessary figure

The bar-mode instability in differentially rotating neutron stars: Simulations in full general relativity

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with differential rotation. We perform fully relativistic 3D simulations of compact stars with $M/R \geq 0.1$, where $M$ is the total gravitational mass and $R$ the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index $\Gamma=2$. As in Newtonian theory, we find that stars above a critical value of $\beta \equiv T/W$ (where $T$ is the rotational kinetic energy and $W$ the gravitational binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation profile, the critical value of $\beta = \beta_{dGR}$ is $\sim 0.24-0.25$, only slightly smaller than the well-known Newtonian value $\sim 0.27$ for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of differential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large $\beta$ subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large $\beta \gtrsim \beta_{dGR}$ do not develop spiral arms or eject mass but adjust to form dynamically stable ellipsoidal-like configurations. If the bar-mode instability is triggered in supernovae collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies.Comment: 17 pages, accepted for publication in AP

Presupernova Evolution of Rotating Massive Stars I: Numerical Method and Evolution of the Internal Stellar Structure

The evolution of rotating stars with zero-age main sequence (ZAMS) masses in the range 8 to 25 M_sun is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70 % of break-up. Redistribution of angular momentum and chemical species are then followed as a consequence of rotationally induced circulation and instablities. The effects of the centrifugal force on the stellar structure are included. Uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (non-magnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlaying material of 1E16...1E17 erg s. These values are insensitive to the initial angular momentum. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to break-up. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.Comment: 62 pages, including 7 tables and 19 figures. Accepted by Ap

Radiative transfer on hierarchial grids

We present new methods for radiative transfer on hierarchial grids. We develop a new method for calculating the scattered flux that employs the grid structure to speed up the computation. We describe a novel subiteration algorithm that can be used to accelerate calculations with strong dust temperature self-coupling. We compute two test models, a molecular cloud and a circumstellar disc, and compare the accuracy and speed of the new algorithms against existing methods. An adaptive model of the molecular cloud with less than 8 % of the cells in the uniform grid produced results in good agreement with the full resolution model. The relative RMS error of the surface brightness <4 % at all wavelengths, and in regions of high column density the relative RMS error was only 10^{-4}. Computation with the adaptive model was faster by a factor of ~5. The new method for calculating the scattered flux is faster by a factor of ~4 in large models with a deep hierarchy structure, when images of the scattered light are computed towards several observing directions. The efficiency of the subiteration algorithm is highly dependent on the details of the model. In the circumstellar disc test the speed-up was a factor of two, but much larger gains are possible. The algorithm is expected to be most beneficial in models where a large number of small, dense regions are embedded in an environment with a lower mean density.Comment: Accepted to A&A; 13 pages, 8 figures; (v2: minor typos corrected

Community Fisheries Development Office (CFDO) strategic plan, January 2004

In October 2000 the government of Cambodia announced a major change in fisheries management policy. The core elements of the new policy are the reduction of fishing lot concession areas by 56%, the broader participation of fishing communities in the management of fisheries and a focus on the efficient, sustainable and equitable use of the living aquatic resources. To facilitate the establishment and development of the Community Fisheries, support and monitor their activities, the Department of Fisheries was authorized1 to establish a Community Fisheries Development Office (CFDO). (Pdf contains 19 pages)

Cloaking and anamorphism for light and mass diffusion

We first review classical results on cloaking and mirage effects for electromagnetic waves. We then show that transformation optics allows the masking of objects or produces mirages in diffusive regimes. In order to achieve this, we consider the equation for diffusive photon density in transformed coordinates, which is valid for diffusive light in scattering media. More precisely, generalizing transformations for star domains introduced in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we numerically demonstrate that infinite conducting objects of different shapes scatter diffusive light in exactly the same way. We also propose a design of external light-diffusion cloak with spatially varying sign-shifting parameters that hides a finite size scatterer outside the cloak. We next analyse non-physical parameter in the transformed Fick's equation derived in [Guenneau and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a non-linear transform that overcomes this problem. We finally investigate other form invariant transformed diffusion-like equations in the time domain, and touch upon conformal mappings and non-Euclidean cloaking applied to diffusion processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas corrected, some extra cases added, overall length extended from 21 pages (V1) to 42 pages (present version V2). The last version will appear at Journal of Optic