204,148 research outputs found
Evolving the Bowen-York initial data for spinning black holes
The Bowen-York initial value data typically used in numerical relativity to
represent spinning black hole are not those of a constant-time slice of the
Kerr spacetime. If Bowen-York initial data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to Kerr form. We compute this radiation by treating the
geometry for a single hole as a perturbation of a Schwarzschild black hole, and
by using second order perturbation theory. We discuss the extent to which
Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi
Bowen-York Tensors
There is derived, for a conformally flat three-space, a family of linear
second-order partial differential operators which send vectors into tracefree,
symmetric two-tensors. These maps, which are parametrized by conformal Killing
vectors on the three-space, are such that the divergence of the resulting
tensor field depends only on the divergence of the original vector field. In
particular these maps send source-free electric fields into TT-tensors.
Moreover, if the original vector field is the Coulomb field on
, the resulting tensor fields on
are nothing but the family of
TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari:
Essays in Honour of Vincent Moncrief
Bowen-York trumpet data and black-hole simulations
The most popular method to construct initial data for black-hole-binary
simulations is the puncture method, in which compactified wormholes are given
linear and angular momentum via the Bowen-York extrinsic curvature. When these
data are evolved, they quickly approach a ``trumpet'' topology, suggesting that
it would be preferable to use data that are in trumpet form from the outset. To
achieve this, we extend the puncture method to allow the construction of
Bowen-York trumpets, including an outline of an existence and uniqueness proof
of the solutions. We construct boosted, spinning and binary Bowen-York puncture
trumpets using a single-domain pseudospectral elliptic solver, and evolve the
binary data and compare with standard wormhole-data results. We also show that
for boosted trumpets the black-hole mass can be prescribed {\it a priori},
without recourse to the iterative procedure that is necessary for wormhole
data.Comment: 15 pages, 14 figures. Published versio
Extreme Bowen-York initial data
The Bowen-York family of spinning black hole initial data depends essentially
on one, positive, free parameter. The extreme limit corresponds to making this
parameter equal to zero. This choice represents a singular limit for the
constraint equations. We prove that in this limit a new solution of the
constraint equations is obtained. These initial data have similar properties to
the extreme Kerr and Reissner-Nordstrom black hole initial data. In particular,
in this limit one of the asymptotic ends changes from asymptotically flat to
cylindrical. The existence proof is constructive, we actually show that a
sequence of Bowen-York data converges to the extreme solution.Comment: 21 page
Nonexistence of conformally flat slices of the Kerr spacetime
Initial data for black hole collisions are commonly generated using the
Bowen-York approach based on conformally flat 3-geometries. The standard
(constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not
conformally flat, so that use of the Bowen-York approach is limited in dealing
with rotating holes. We investigate here whether there exist foliations of the
Kerr spacetime that are conformally flat. We limit our considerations to
foliations that are axisymmetric and that smoothly reduce in the Schwarzschild
limit to slices of constant Schwarzschild time. With these restrictions, we
show that no conformally flat slices can exist.Comment: 5 LaTeX pages; no figures; to be submitted to Phys. Rev.
Evolving the Bowen-York initial data for spinning black holes
The Bowen-York initial value data typically used in numerical relativity to represent a spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the “relaxation” of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes. © 1998 The American Physical Society
New conformally flat initial data for spinning black holes
We obtain an explicit solution of the momentum constraint for conformally
flat, maximal slicing, initial data which gives an alternative to the purely
longitudinal extrinsic curvature of Bowen and York. The new solution is
related, in a precise form, with the extrinsic curvature of a Kerr slice. We
study these new initial data representing spinning black holes by numerically
solving the Hamiltonian constraint. They have the following features: i)
Contain less radiation, for all allowed values of the rotation parameter, than
the corresponding single spinning Bowen-York black hole. ii) The maximum
rotation parameter reached by this solution is higher than that of the
purely longitudinal solution allowing thus to describe holes closer to a
maximally rotating Kerr one. We discuss the physical interpretation of these
properties and their relation with the weak cosmic censorship conjecture.
Finally, we generalize the data for multiple black holes using the ``puncture''
and isometric formulations.Comment: 6 pages, 4 figures, RevTeX
Tidal deformations of spinning black holes in Bowen-York initial data
We study the tidal deformations of the shape of a spinning black hole horizon
due to a binary companion in the Bowen-York initial data set. We use the
framework of quasi-local horizons and identify a black hole by marginally outer
trapped surfaces. The intrinsic horizon geometry is specified by a set of mass
and angular-momentum multipole moments and
respectively.
The tidal deformations are described by the change in these multipole moments
caused by an external perturbation. This leads us to define two sets of
dimensionless numbers, the tidal coefficients for and
, which specify the deformations of a black hole with a binary
companion. We compute these tidal coefficients in a specific model problem,
namely the Bowen-York initial data set for binary black holes. We restrict
ourselves to axisymmetric situations and to small spins. Within this
approximation, we analytically compute the conformal factor, the location of
the marginally trapped surfaces, and finally the multipole moments and the
tidal coefficients.Comment: 22 pages, 1 figur
Existence and uniqueness of Bowen-York Trumpets
We prove the existence of initial data sets which possess an asymptotically
flat and an asymptotically cylindrical end. Such geometries are known as
trumpets in the community of numerical relativists.Comment: This corresponds to the published version in Class. Quantum Grav. 28
(2011) 24500
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