Approximate Killing vectors on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>S</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>

Cook, G.G.; Whiting, B. F.

doi:10.1103/physrevd.76.041501

Cited by 72 publications

(99 citation statements)

References 9 publications

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“…This physical spin configuration will generally be slightly different than the one relativists had intended to specify, introducing error into the initial spin components {a i }. Techniques exist to measure BBH spins in simulations [18,59,60,61,62], so one could measure the initial spins after the junk radiation had exited the system, and use these components rather than those supposedly specified by the numerical initial data. However, while at large binary separations the initial spin components of the two black holes are well defined, at finite separations the components are gaugedependent and different techniques for measuring them yield different results.…”

Section: Including Initial Spin Uncertaintiesmentioning

confidence: 99%

Spin expansion for binary black hole mergers: New predictions and future directions

Boyle

Kesden

2008

Phys. Rev. D

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In a recent paper [1], we introduced a spin expansion that provides a simple yet powerful way to understand aspects of binary black hole (BBH) merger. This approach relies on the symmetry properties of initial and final quantities like the black hole mass m, kick velocity k, and spin vector s, rather than a detailed understanding of the merger dynamics. In this paper, we expand on this proposal, examine how well its predictions agree with current simulations, and discuss several future directions that would make it an even more valuable tool. The spin expansion yields many new predictions, including several exact results that may be useful for testing numerical codes. Some of these predictions have already been confirmed, while others await future simulations. We explain how a relatively small number of simulations -10 equal-mass simulations, and 16 unequal-mass simulations -may be used to calibrate all of the coefficients in the spin expansion up to second order at the minimum computational cost. For a more general set of simulations of given covariance, we derive the minimum-variance unbiased estimators for the spin expansion coefficients. We discuss how this calibration would be interesting and fruitful for general relativity and astrophysics. Finally, we sketch the extension to eccentric orbits.

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Section: Including Initial Spin Uncertaintiesmentioning

confidence: 99%

Spin expansion for binary black hole mergers: New predictions and future directions

Boyle

Kesden

2008

Phys. Rev. D

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“…A similar method can be found in the appendix of [46], for an application to a BBH simulation see [16]. Recently Beetle [47] pointed out that Cook's [38] approach is closely related to an older proposal by Matzner [36], where the aKVF is the solution of an eigenvalue problem. An outstanding question is still the normalization of these aKVFs.…”

Section: B Approximate Killing Vector Fieldsmentioning

confidence: 99%

“…Another approach to find an approximate Killing vector field has been given by [38]. They use a variational principle to minimize the 'non-symmetric' features of the vector field.…”

Section: B Approximate Killing Vector Fieldsmentioning

confidence: 99%

“…where dA is the 2D area element, K ij the extrinsic curvature of the Cauchy slice and s i is the outward-pointing surface normal on the MOTS denoted by S. In order to obtain Φ j the 2D Killing equation has to be solved; if the axisymmetry is perturbed approximate KVFs (aKVFs) have to be computed [36,37,38], for applications in BBH simulations see [11,16]. Sometimes, due to computational reasons, the effort of finding a KVF or aKVF is not done and coordinate vector fields are instead used to estimate…”

Section: Introductionmentioning

confidence: 99%

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A new method for computing quasi-local spin and other invariants on marginally trapped surfaces

Jasiulek¹

2009

Class. Quantum Grav.

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We accurately compute the scalar 2-curvature, the Weyl scalars, associated quasi-local spin, mass and higher multipole moments on marginally trapped surfaces in numerical 3+1 simulations. To determine the quasi-local quantities we introduce a new method which requires a set of invariant surface integrals, allowing for surface grids of a few hundred points only. The new technique circumvents solving the Killing equation and is also an alternative to approximate Killing vector fields. We apply the method to a perturbed non-axisymmetric black hole ringing down to Kerr and compare the quasi-local spin with other methods that use Killing vector fields, coordinate vector fields, quasinormal ringing and properties of the Kerr metric on the surface. Interesting is the agreement with the spin of approximate Killing vector fields during the phase of perturbed axisymmetry. Additionally, we introduce a new coordinate transformation, adapting spherical coordinates to any two points on the sphere like the two minima of the scalar 2-curvature on axisymmetric trapped surfaces.

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“…We thus need to find the value that makes the BH spin vanish. To compute the spin, we use approximate Killing vectors on the apparent horizon, following a method [39] similar to the work of Cook and Whiting [40].…”

Section: E Observing Physical Quantitiesmentioning

confidence: 99%

Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method

et al. 2008

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We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to construct high-accuracy solutions at a relatively low computational cost. We provide convergence tests of the method for both isolated neutron stars and irrotational binaries. In the second case, we show that we can resolve the small inconsistencies that are part of the quasiequilibrium formulation, and that these inconsistencies are significantly smaller than observed in previous works. The possibility of generating a wide variety of initial data is also demonstrated through two new configurations inspired by results from binary black holes. First, we show that choosing a modified Kerr-Schild conformal metric instead of a flat conformal metric allows for the construction of quasiequilibrium binaries with a spinning black hole. Second, we construct binaries in low-eccentricity orbits, which are a better approximation to astrophysical binaries than quasiequilibrium systems.

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Approximate Killing vectors onS2

Cited by 72 publications

References 9 publications

Spin expansion for binary black hole mergers: New predictions and future directions

Spin expansion for binary black hole mergers: New predictions and future directions

A new method for computing quasi-local spin and other invariants on marginally trapped surfaces

Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method

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