Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral

Standard choices of quasi-circular orbit parameters for black-hole binary evolutions result in eccentric inspiral. We introduce a conceptually simple method, which is to integrate the post-Newtonian equations of motion through hundreds of orbits, and read off the values of the momenta at the separation at which we wish to start a fully general relativistic numerical evolution. For the particular case of non-spinning equal-mass inspiral with an initial coordinate separation of $D = 11M$ we show that this approach reduces the eccentricity by at least a factor of five to $e < 0.002$ as compared to using standard quasi-circular initial parameters.Comment: 6 pages, 3 figures, 1 tabl

What should religious education aim to achieve?: An investigation into the purpose of religious education in the public sphere

This thesis is concerned with the question of what religious education should aim to achieve in the public sphere, and from that comes an interest in what is it that the teacher of religious education should aim to do. My enquiry is located, theoretically as well as conceptually, in the sphere of education. It is an educational study into religious education and situated in what can be termed a ‘Continental construction’ of educational research. I identify that since the inception of religious education in public schools in England, persistent assumptions have been made about both religion and education. I show how this has led, in my view, to conceptualisations of religious education which have been, and continue to be, incomplete. The central chapters of my thesis consider first religion and then education. This allows me to introduce my theoretical base, which is especially but not exclusively drawn from the work of Simone Weil and Hannah Arendt. I develop an argument suggesting that by also understanding religion existentially as faith, rather than as only belief or practice, will open new ways of considering the role of religious education in the public sphere. This is alongside an argument I develop with Arendt for education being conceptualised as bringing the child to action rather than to reason. This thesis argues for a broader understanding of religion, and therefore what it means to live a religious life, in religious education than has previously been considered. I bring this broader way of understanding what it means to live a religious life together with my argument for conceptualising education as bringing the child to action. This enables me to make a new proposal for what religious education should aim to achieve in the public sphere

Beyond the Bowen-York extrinsic curvature for spinning black holes

It is well-known that Bowen-York initial data contain spurious radiation. Although this ``junk'' radiation has been seen to be small for non-spinning black-hole binaries in circular orbit, its magnitude increases when the black holes are given spin. It is possible to reduce the spurious radiation by applying the puncture approach to multiple Kerr black holes, as we demonstrate for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical Relativity" issue of Classical and Quantum Gravit

Ringdown frequencies in black holes formed from precessing black-hole binaries

We present a simple formula for the effective ringdown frequencies of the gravitational-wave signal of a precessing black-hole binary in the coprecessing frame. This formula requires only knowledge of the quasi-normal mode frequencies of the system and the value of the precession angle β during ringdown. Such a formula will be useful in modeling precessing systems. We also provide a comprehensive description of the oscillations in the ringdown frequency in an inertial frame where the spin of the final black hole is in the z-direction. These oscillations arise due to the superposition of the prograde and retrograde frequencies. Our understanding of these oscillations can be used to extract the ratio of the amplitudes of the prograde and retrograde frequencies from numerical data. Alternatively, knowledge of this ratio of the amplitudes can be used to produce a simple model of the time-domain oscillations in the ringdown frequency

Modeling the gravitational wave signature of neutron star black hole coalescences: PhenomNSBH

Accurate gravitational-wave (GW) signal models exist for black-hole binary (BBH) and neutron-star binary (BNS) systems, which are consistent with all of the published GW observations to date. Detections of a third class of compact-binary systems, neutron-star-black-hole (NSBH) binaries, have not yet been confirmed, but are eagerly awaited in the near future. For NSBH systems, GW models do not exist across the viable parameter space of signals. In this work we present the frequency-domain phenomenological model, PhenomNSBH, for GWs produced by NSBH systems with mass ratios from equal-mass up to 15, spin on the black hole up to a dimensionless spin of $|\chi|=0.5$, and tidal deformabilities ranging from 0 (the BBH limit) to 5000. We extend previous work on a phenomenological amplitude model for NSBH systems to produce an amplitude model that is parameterized by a single tidal deformability parameter. This amplitude model is combined with an analytic phase model describing tidal corrections. The resulting approximant is accurate enough to be used to measure the properties of NSBH systems for signal-to-noise ratios (SNRs) up to 50, and is compared to publicly-available NSBH numerical-relativity simulations and hybrid waveforms constructed from numerical-relativity simulations and tidal inspiral approximants. For most signals observed by second-generation ground-based detectors within this SNR limit, it will be difficult to use the GW signal alone to distinguish single NSBH systems from either BNSs or BBHs, and therefore to unambiguously identify an NSBH system

BSSN in Spherical Symmetry

The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth--order finite difference implementation of the equations.Comment: This is the final version to be published in CQG. It contains much more information and detail than the original 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