235 research outputs found
Finding Apparent Horizons in Dynamic 3D Numerical Spacetimes
We have developed a general method for finding apparent horizons in 3D
numerical relativity. Instead of solving for the partial differential equation
describing the location of the apparent horizons, we expand the closed 2D
surfaces in terms of symmetric trace--free tensors and solve for the expansion
coefficients using a minimization procedure. Our method is applied to a number
of different spacetimes, including numerically constructed spacetimes
containing highly distorted axisymmetric black holes in spherical coordinates,
and 3D rotating, and colliding black holes in Cartesian coordinates.Comment: 19 pages, 13 figures, LaTex, to appear in Phys. Rev. D. Minor changes
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New Coordinate Systems for Axisymmetric Black Hole Collisions
We describe a numerical grid generating procedure to construct new classes of
orthogonal coordinate systems that are specially adapted to binary black hole
spacetimes. The new coordinates offer an alternative approach to the
conventional \v{C}ade\v{z} coordinates, in addition to providing a potentially
more stable and flexible platform to extend previous calculations of binary
black hole collisions.Comment: 3 pages, 5 postscript figures, LaTeX, uses mprocl.sty (available at
http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the
proceedings of the Marcel Grossmann 8 (Jerusalem, 1997
Tracking Black Holes in Numerical Relativity
This work addresses and solves the problem of generically tracking black hole
event horizons in computational simulation of black hole interactions.
Solutions of the hyperbolic eikonal equation, solved on a curved spacetime
manifold containing black hole sources, are employed in development of a robust
tracking method capable of continuously monitoring arbitrary changes of
topology in the event horizon, as well as arbitrary numbers of gravitational
sources. The method makes use of continuous families of level set viscosity
solutions of the eikonal equation with identification of the black hole event
horizon obtained by the signature feature of discontinuity formation in the
eikonal's solution. The method is employed in the analysis of the event horizon
for the asymmetric merger in a binary black hole system. In this first such
three dimensional analysis, we establish both qualitative and quantitative
physics for the asymmetric collision; including: 1. Bounds on the topology of
the throat connecting the holes following merger, 2. Time of merger, and 3.
Continuous accounting for the surface of section areas of the black hole
sources.Comment: 14 pages, 16 figure
An ellipsoidal mirror for focusing neutral atomic and molecular beams
Manipulation of atomic and molecular beams is essential to atom optics applications including atom lasers, atom lithography, atom interferometry and neutral atom microscopy. The manipulation of charge-neutral beams of limited polarizability, spin or excitation states remains problematic, but may be overcome by the development of novel diffractive or reflective optical elements. In this paper, we present the first experimental demonstration of atom focusing using an ellipsoidal mirror. The ellipsoidal mirror enables stigmatic off-axis focusing for the first time and we demonstrate focusing of a beam of neutral, ground-state helium atoms down to an approximately circular spot, (26.8±0.5) μm×(31.4±0.8) μm in size. The spot area is two orders of magnitude smaller than previous reflective focusing of atomic beams and is a critical milestone towards the construction of a high-intensity scanning helium microscope
Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity
We describe a numerical code that solves Einstein's equations for a
Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation
introduced by Choquet-Bruhat and York. This is the first time this formulation
has been used to evolve a numerical spacetime containing a black hole. We
excise the hole from the computational grid in order to avoid the central
singularity. We describe in detail a causal differencing method that should
allow one to stably evolve a hyperbolic system of equations in three spatial
dimensions with an arbitrary shift vector, to second-order accuracy in both
space and time. We demonstrate the success of this method in the spherically
symmetric case.Comment: 23 pages RevTeX plus 7 PostScript figures. Submitted to Phys. Rev.
Adaptive Event Horizon Tracking and Critical Phenomena in Binary Black Hole Coalescence
This work establishes critical phenomena in the topological transition of
black hole coalescence. We describe and validate a computational front tracking
event horizon solver, developed for generic studies of the black hole
coalescence problem. We then apply this to the Kastor - Traschen axisymmetric
analytic solution of the extremal Maxwell - Einstein black hole merger with
cosmological constant. The surprising result of this computational analysis is
a power law scaling of the minimal throat proportional to time. The minimal
throat connecting the two holes obeys this power law during a short time
immediately at the beginning of merger. We also confirm the behavior
analytically. Thus, at least in one axisymmetric situation a critical
phenomenon exists. We give arguments for a broader universality class than the
restricted requirements of the Kastor - Traschen solution.Comment: 13 pages, 20 figures Corrected labels on figures 17 through 20.
Corrected typos in references. Added some comment
Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence
We describe the null geometry of a multiple black hole event horizon in terms
of a conformal rescaling of a flat space null hypersurface. For the prolate
spheroidal case, we show that the method reproduces the pair-of-pants shaped
horizon found in the numerical simulation of the head-on-collision of black
holes. For the oblate case, it reproduces the initially toroidal event horizon
found in the numerical simulation of collapse of a rotating cluster. The
analytic nature of the approach makes further conclusions possible, such as a
bearing on the hoop conjecture. From a time reversed point of view, the
approach yields a description of the past event horizon of a fissioning white
hole, which can be used as null data for the characteristic evolution of the
exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.
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