11 research outputs found
Locating Boosted Kerr and Schwarzschild Apparent Horizons
We describe a finite-difference method for locating apparent horizons and
illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our
model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to
this spacetime metric and then carry out a 3+1 decomposition. The result is a
slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz
contracted. We show that our method can locate distorted apparent horizons
efficiently and accurately.Comment: Submitted to Physical Review D. 12 pages and 22 figure
Finding apparent horizons and other two-surfaces of constant expansion
Apparent horizons are structures of spacelike hypersurfaces that can be
determined locally in time. Closed surfaces of constant expansion (CE surfaces)
are a generalisation of apparent horizons. I present an efficient method for
locating CE surfaces. This method uses an explicit representation of the
surface, allowing for arbitrary resolutions and, in principle, shapes. The CE
surface equation is then solved as a nonlinear elliptic equation.
It is reasonable to assume that CE surfaces foliate a spacelike hypersurface
outside of some interior region, thus defining an invariant (but still
slicing-dependent) radial coordinate. This can be used to determine gauge modes
and to compare time evolutions with different gauge conditions. CE surfaces
also provide an efficient way to find new apparent horizons as they appear e.g.
in binary black hole simulations.Comment: 21 pages, 8 figures; two references adde
Boosted three-dimensional black-hole evolutions with singularity excision
Binary black hole interactions provide potentially the strongest source of
gravitational radiation for detectors currently under development. We present
some results from the Binary Black Hole Grand Challenge Alliance three-
dimensional Cauchy evolution module. These constitute essential steps towards
modeling such interactions and predicting gravitational radiation waveforms. We
report on single black hole evolutions and the first successful demonstration
of a black hole moving freely through a three-dimensional computational grid
via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of
duration ~60M
Gravitational wave extraction and outer boundary conditions by perturbative matching
We present a method for extracting gravitational radiation from a
three-dimensional numerical relativity simulation and, using the extracted
data, to provide outer boundary conditions. The method treats dynamical
gravitational variables as nonspherical perturbations of Schwarzschild
geometry. We discuss a code which implements this method and present results of
tests which have been performed with a three dimensional numerical relativity
code
Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes
We report new results which establish that the accurate 3-dimensional
numerical simulation of generic single-black-hole spacetimes has been achieved
by characteristic evolution with unlimited long term stability. Our results
cover a selection of distorted, moving and spinning single black holes, with
evolution times up to 60,000M.Comment: 4 pages, 3 figure
Gravitational wave extraction and outer boundary conditions by perturbative matching
We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code
Numerical Relativity: A review
Computer simulations are enabling researchers to investigate systems which
are extremely difficult to handle analytically. In the particular case of
General Relativity, numerical models have proved extremely valuable for
investigations of strong field scenarios and been crucial to reveal unexpected
phenomena. Considerable efforts are being spent to simulate astrophysically
relevant simulations, understand different aspects of the theory and even
provide insights in the search for a quantum theory of gravity. In the present
article I review the present status of the field of Numerical Relativity,
describe the techniques most commonly used and discuss open problems and (some)
future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and
Quantum Gravity. (uses iopart.cls