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

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

Review of the Laguerre-Gauss mode technology research program at Birmingham

Gravitational wave detectors from the advanced generation onwards are expected to be limited in sensitivity by thermal noise of the optics, making the reduction of this noise a key factor in the success of such detectors. A proposed method for reducing the impact of this noise is to use higher-order Laguerre-Gauss (LG) modes for the readout beam, as opposed to the currently used fundamental mode. We present here a synopsis of the research program undertaken by the University of Birmingham into the suitability of LG mode technology for future gravitational wave detectors. This will cover our previous and current work on this topic, from initial simulations and table-top LG mode experiments up to implementation in a prototype scale suspended cavity and high-power laser bench

Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure removed due to page limitatio

Are moving punctures equivalent to moving black holes?

When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one ``excises'' a spatial neighbourhood of the singularity from the numerical grid on each spacelike hypersurface. A second and more recent one, instead, begins with a ``puncture'' solution and then evolves the full 3-metric, including the singular point. In the continuum limit, excision is justified by the light-cone structure of the Einstein equations and, in practice, can give accurate numerical solutions when suitable discretizations are used. However, because the field variables are non-differentiable at the puncture, there is no proof that the moving-punctures technique is correct, particularly in the discrete case. To investigate this question we use both techniques to evolve a binary system of equal-mass non-spinning black holes. We compare the evolution of two curvature 4-scalars with proper time along the invariantly-defined worldline midway between the two black holes, using Richardson extrapolation to reduce the influence of finite-difference truncation errors. We find that the excision and moving-punctures evolutions produce the same invariants along that worldline, and thus the same spacetimes throughout that worldline's causal past. This provides convincing evidence that moving-punctures are indeed equivalent to moving black holes.Comment: 4 pages, 3 eps color figures; v2 = major revisions to introduction & conclusions based on referee comments, but no change in analysis or result

Method to estimate ISCO and ring-down frequencies in binary systems and consequences for gravitational wave data analysis

Recent advances in the description of compact binary systems have produced gravitational waveforms that include inspiral, merger and ring-down phases. Comparing results from numerical simulations with those of post-Newtonian (PN), and related, expansions has provided motivation for employing PN waveforms in near merger epochs when searching for gravitational waves and has encouraged the development of analytic fits to full numerical waveforms. The models and simulations do not yet cover the full binary coalescence parameter space. For these yet un-simulated regions, data analysts can still conduct separate inspiral, merger and ring-down searches. Improved knowledge about the end of the inspiral phase, the beginning of the merger, and the ring-down frequencies could increase the efficiency of both coherent inspiral-merger-ring-down (IMR) searches and searches over each phase separately. Insight can be gained for all three cases through a recently presented theoretical calculation, which, corroborated by the numerical results, provides an implicit formula for the final spin of the merged black holes, accurate to within 10% over a large parameter space. Knowledge of the final spin allows one to predict the end of the inspiral phase and the quasinormal mode ring-down frequencies, and in turn provides information about the bandwidth and duration of the merger. In this work we will discuss a few of the implications of this calculation for data analysis.Comment: Added references to section 3 14 pages 5 figures. Submitted to Classical and Quantum Gravit

Conformally flat black hole initial data, with one cylindrical end

We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's initial data. This extends and refines a previous result \cite{dain-gabach09} to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published version in Class. Quantum Grav. (2010). Results unchange

Complete phenomenological gravitational waveforms from spinning coalescing binaries

The quest for gravitational waves from coalescing binaries is customarily performed by the LIGO-Virgo collaboration via matched filtering, which requires a detailed knowledge of the signal. Complete analytical coalescence waveforms are currently available only for the non-precessing binary systems. In this paper we introduce complete phenomenological waveforms for the dominant quadrupolar mode of generically spinning systems. These waveforms are constructed by bridging the gap between the analytically known inspiral phase, described by spin Taylor (T4) approximants in the restricted waveform approximation, and the ring-down phase through a phenomenological intermediate phase, calibrated by comparison with specific, numerically generated waveforms, describing equal mass systems with dimension-less spin magnitudes equal to 0.6. The overlap integral between numerical and phenomenological waveforms ranges between 0.95 and 0.99.Comment: Proceeding for the GWDAW-14 conference. Added reference in v

Phenomenological template family for black-hole coalescence waveforms

Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger, and ring-down stages of black hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.Comment: Minor changes, Submitted to Class. Quantum Grav. (Proc. GWDAW11