Implementing an apparent-horizon finder in three dimensions

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures

Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity

We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the surface of an excised sphere (the apparent horizon). In this paper we focus on irrotational configurations, meaning that both the neutron star and the black hole are approximately nonspinning in an inertial frame. We present results for a binary with polytropic index n=1, mass ratio M_{irr}^{BH}/M_{B}^{NS}=5 and neutron star compaction M_{ADM,0}^{NS}/R_0=0.0879, where M_{irr}^{BH} is the irreducible mass of the black hole, M_{B}^{NS} the neutron star baryon rest-mass, and M_{ADM,0}^{NS} and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in isolation, respectively. Our models represent valid solutions to Einstein's constraint equations and may therefore be employed as initial data for dynamical simulations of black hole-neutron star binaries.Comment: 5 pages, 1 figure, revtex4, published in Phys.Rev.

Quasiequilibrium black hole-neutron star binaries in general relativity

We construct quasiequilibrium sequences of black hole-neutron star binaries in general relativity. We solve Einstein's constraint equations in the conformal thin-sandwich formalism, subject to black hole boundary conditions imposed on the surface of an excised sphere, together with the relativistic equations of hydrostatic equilibrium. In contrast to our previous calculations we adopt a flat spatial background geometry and do not assume extreme mass ratios. We adopt a Gamma=2 polytropic equation of state and focus on irrotational neutron star configurations as well as approximately nonspinning black holes. We present numerical results for ratios of the black hole's irreducible mass to the neutron star's ADM mass in isolation of M_{irr}^{BH}/M_{ADM,0}^{NS} = 1, 2, 3, 5, and 10. We consider neutron stars of baryon rest mass M_B^{NS}/M_B^{max} = 83% and 56%, where M_B^{max} is the maximum allowed rest mass of a spherical star in isolation for our equation of state. For these sequences, we locate the onset of tidal disruption and, in cases with sufficiently large mass ratios and neutron star compactions, the innermost stable circular orbit. We compare with previous results for black hole-neutron star binaries and find excellent agreement with third-order post-Newtonian results, especially for large binary separations. We also use our results to estimate the energy spectrum of the outgoing gravitational radiation emitted during the inspiral phase for these binaries.Comment: 17 pages, 15 figures, published in Phys. Rev.

Black Hole-Neutron Star Binaries in General Relativity: Quasiequilibrium Formulation

We present a new numerical method for the construction of quasiequilibrium models of black hole-neutron star binaries. We solve the constraint equations of general relativity, decomposed in the conformal thin-sandwich formalism, together with the Euler equation for the neutron star matter. We take the system to be stationary in a corotating frame and thereby assume the presence of a helical Killing vector. We solve these coupled equations in the background metric of a Kerr-Schild black hole, which accounts for the neutron star's black hole companion. In this paper we adopt a polytropic equation of state for the neutron star matter and assume large black hole--to--neutron star mass ratios. These simplifications allow us to focus on the construction of quasiequilibrium neutron star models in the presence of strong-field, black hole companions. We summarize the results of several code tests, compare with Newtonian models, and locate the onset of tidal disruption in a fully relativistic framework.Comment: 17 pages, 7 figures; added discussion, tables; PRD in pres

Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity

We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $\Gamma = 2$ and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion (e.g. via a phase transition) or mass accretion. In no case do we find evidence for the formation of massive disks or any ejecta around the newly formed Kerr black holes, even though the progenitors are rapidly rotating.Comment: 16 pages, to appear in Phys. Rev.

Gravitational Wavetrains in the Quasi-Equilibrium Approximation: A Model Problem in Scalar Gravitation

A quasi-equilibrium (QE) computational scheme was recently developed in general relativity to calculate the complete gravitational wavetrain emitted during the inspiral phase of compact binaries. The QE method exploits the fact that the the gravitational radiation inspiral timescale is much longer than the orbital period everywhere outside the ISCO. Here we demonstrate the validity and advantages of the QE scheme by solving a model problem in relativistic scalar gravitation theory. By adopting scalar gravitation, we are able to numerically track without approximation the damping of a simple, quasi-periodic radiating system (an oscillating spherical matter shell) to final equilibrium, and then use the exact numerical results to calibrate the QE approximation method. In particular, we calculate the emitted gravitational wavetrain three different ways: by integrating the exact coupled dynamical field and matter equations, by using the scalar-wave monopole approximation formula (corresponding to the quadrupole formula in general relativity), and by adopting the QE scheme. We find that the monopole formula works well for weak field cases, but fails when the fields become even moderately strong. By contrast, the QE scheme remains quite reliable for moderately strong fields, and begins to breakdown only for ultra-strong fields. The QE scheme thus provides a promising technique to construct the complete wavetrain from binary inspiral outside the ISCO, where the gravitational fields are strong, but where the computational resources required to follow the system for more than a few orbits by direct numerical integration of the exact equations are prohibitive.Comment: 15 pages, 14 figure

ELN and FBN2 gene variants as risk factors for two sports-related musculoskeletal injuries

The proteins ELN and FBN2 are important in extracellular matrix function. The ELN rs2071307 and FBN2 rs331079 gene variants have been associated with soft tissue pathologies. We aimed to determine whether these variants were predisposing factors for both Achilles tendinopathy (AT) and anterior cruciate ligament (ACL) ruptures. For the AT study, 135 cases (TEN group) and 239 asymptomatic controls were recruited. For the ACL rupture study our cohort consisted of 141 cases (ACL group) and 219 controls. Samples were genotyped for both the ELN rs2071307 and FBN2 rs331079 variants using TaqMan assays. Analysis of variance and chi-squared tests were used to determine whether either variant was associated with AT or ACL rupture with significance set at p<0.05. The GG genotype of the FBN2 variant was significantly over-represented within the TEN group (p=0.035; OR=1.83; 95% CI 1.04–3.25) compared to the CON group. We also found that the frequency of the G allele was significantly different between the TEN (p=0.017; OR=1.90; 95% CI 1.11–3.27) and ACL groups (p=0.047; OR=1.76; 95% CI 1.00–3.10) compared to controls. The ELN rs207137 variant was not associated with either AT or ACL rupture. In conclusion, DNA sequence variation within the FBN2 gene is associated with both AT and ACL rupture

Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral

We present a new method for generating the nonlinear gravitational wavetrain from the late inspiral (pre-coalescence) phase of a binary neutron star system by means of a numerical evolution calculation in full general relativity. In a prototype calculation, we produce 214 wave cycles from corotating polytropes, representing the final part of the inspiral phase prior to reaching the ISCO. Our method is based on the inequality that the orbital decay timescale due to gravitational radiation is much longer than an orbital period and the approximation that gravitational radiation has little effect on the structure of the stars. We employ quasi-equilibrium sequences of binaries in circular orbit for the matter source in our field evolution code. We compute the gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set of binary separations. From these data, we construct the gravitational waveform as a continuous wavetrain. Finally, we discuss the limitations of our current calculation, planned improvements, and potential applications of our method to other inspiral scenarios.Comment: 4 pages, 4 figure