Alternatives to standard puncture initial data for binary black hole evolution

Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of spurious radiation. We study the evolution of three alternative initial data schemes. Two of the three alternatives are based on post-Newtonian expansions that contain realistic gravitational waves. The first scheme is based on a second-order post-Newtonian expansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been resummed to approach standard puncture data at the black holes. The second scheme is based on asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a first-order post-Newtonian expansion in ADMTT gauge away from the black holes. The final alternative is obtained through asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a second-order post-Newtonian expansion in harmonic gauge away from the black holes. When evolved, the second scheme fails to produce quasicircular orbits (and instead leads to a nearly head-on collision). This failure can be traced back to inaccuracies in the extrinsic curvature due to low order matching. More encouraging is that the latter two alternatives lead to quasicircular orbits and show gravitational radiation from the onset of the evolution, as well as a reduction of spurious radiation. Current deficiencies compared to standard punctures data include more eccentric trajectories during the inspiral and larger constraint violations, since the alternative data sets are only approximate solutions of Einstein's equations. The eccentricity problem can be ameliorated by adjusting the initial momentum parameters.Comment: 11 pages, 11 figures, 1 appendix, typos corrected, removed duplicate reference, matches published versio

Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.Comment: 6 pages, 3 figures, 1 tabl

A new numerical method to construct binary neutron star initial data

We present a new numerical method for the generation of binary neutron star initial data using a method along the lines of the the Wilson-Mathews or the closely related conformal thin sandwich approach. Our method uses six different computational domains, which include spatial infinity. Each domain has its own coordinates which are chosen such that the star surfaces always coincide with domain boundaries. These properties facilitate the imposition of boundary conditions. Since all our fields are smooth inside each domain, we are able to use an efficient pseudospectral method to solve the elliptic equations associated with the conformal thin sandwich approach. Currently we have implemented corotating configurations with arbitrary mass ratios, but an extension to arbitrary spins is possible. The main purpose of this paper is to introduce our new method and to test our code for several different configurations.Comment: 18 pages, 8 figures, 1 tabl

Black hole puncture initial data with realistic gravitational wave content

We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining integral terms. These terms improve accuracy in the far zone and, for the first time, include realistic gravitational waves in the initial data. We investigate the behavior of these data both at the center of mass and in the far zone, demonstrating agreement of the transverse-traceless parts of the new metric with quadrupole-approximation waveforms. These data can be used for numerical evolutions, enabling a direct connection between the merger waveforms and the post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio

A single-domain spectral method for black hole puncture data

We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these methods exhibit rapid convergence of the conformal factor and lead to highly accurate solutions. As an application we investigate small mass ratios of binary black holes and compare these with the corresponding test mass limit that we obtain through a semi-analytical limiting procedure. In particular, we compare the binding energy of puncture data in this limit with that of a test particle in the Schwarzschild spacetime and find that it deviates by 50% from the Schwarzschild result at the innermost stable circular orbit of Schwarzschild, if the ADM mass at each puncture is used to define the local black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see Fig. 4 and the corresponding changes to the tex

Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in ADMTT coordinates. The specific matching procedure used here closely follows the calculation in gr-qc/0503011, and is performed in the so called buffer zone where both the post-Newtonian and the perturbed Schwarzschild approximations hold. The result is that both metrics agree in the buffer zone, up to the errors in the approximations. However, since isotropic coordinates are very similar to ADMTT coordinates, matching yields better results than in the previous calculation, where harmonic coordinates were used for the post-Newtonian 4-metric. In particular, not only does matching improve in the buffer zone, but due to the similarity between ADMTT and isotropic coordinates the two metrics are also close to each other near the black hole horizons. With the help of a transition function we also obtain a global smooth 4-metric which has errors on the order of the error introduced by the more accurate of the two approximations we match. This global smoothed out 4-metric is obtained in ADMTT coordinates which are not horizon penetrating. In addition, we construct a further coordinate transformation that takes the 4-metric from global ADMTT coordinates to new coordinates which are similar to Kerr-Schild coordinates near each black hole, but which remain ADMTT further away from the black holes. These new coordinates are horizon penetrating and lead, for example, to a lapse which is everywhere positive on the t=0 slice. Such coordinates may be more useful in numerical simulations.Comment: 25 pages, 21 figures. Replaced with accepted versio

Binary black holes on a budget: Simulations using workstations

Binary black hole simulations have traditionally been computationally very expensive: current simulations are performed in supercomputers involving dozens if not hundreds of processors, thus systematic studies of the parameter space of binary black hole encounters still seem prohibitive with current technology. Here we show how the multi-layered refinement level code BAM can be used on dual processor workstations to simulate certain binary black hole systems. BAM, based on the moving punctures method, provides grid structures composed of boxes of increasing resolution near the center of the grid. In the case of binaries, the highest resolution boxes are placed around each black hole and they track them in their orbits until the final merger when a single set of levels surrounds the black hole remnant. This is particularly useful when simulating spinning black holes since the gravitational fields gradients are larger. We present simulations of binaries with equal mass black holes with spins parallel to the binary axis and intrinsic magnitude of S/m^2= 0.75. Our results compare favorably to those of previous simulations of this particular system. We show that the moving punctures method produces stable simulations at maximum spatial resolutions up to M/160 and for durations of up to the equivalent of 20 orbital periods.Comment: 20 pages, 8 figures. Final version, to appear in a special issue of Class. Quantum Grav. based on the New Frontiers in Numerical Relativity Conference, Golm, July 200

Constructing binary neutron star initial data with high spins, high compactnesses, and high mass ratios

The construction of accurate and consistent initial data for various binary parameters is a critical ingredient for numerical relativity simulations of the compact binary coalescence. In this article, we present an upgrade of the pseudospectral SGRID code, which enables us to access even larger regions of the binary neutron star parameter space. As a proof of principle, we present a selected set of first simulations based on initial configurations computed with the new code version. In particular, we simulate two millisecond pulsars close to their breakup spin, highly compact neutron stars with masses at about $98\%$ of the maximum supported mass of the employed equation of state, and an unequal mass systems with mass ratios even outside the range predicted by population synthesis models ($q = 2.03$). The discussed code extension will help us to simulate previously unexplored binary configurations. This is a necessary step to construct and test new gravitational wave approximants and to interpret upcoming binary neutron star merger observations. When we construct initial data, one has to specify various parameters, such as a rotation parameter for each star. Some of these parameters do not have direct physical meaning, which makes comparisons with other methods or models difficult. To facilitate this, we introduce simple estimates for the initial spin, momentum, mass, and center of mass of each individual star

Binary black hole initial data from matched asymptotic expansions

We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^\infty$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be sraightforwardly iterated to obtain initial data to higher perturbative order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing of text, no major change to the physic

STUDY OF THE LEUKOCYTE MIGRATION INHIBITORY FACTOR IN HUMAN GLOMERULONEPHRITIS FROM THE ASPECT OF THE PROGNOSIS

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