Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-09-28
Class.Quant.Grav. 19 (2002) 375-392
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, 12 figures. Includes comments made by referees
Scientific paper
10.1088/0264-9381/19/2/311
The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat space when such a embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing for the differences between the metric on the original surface and the metric on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of back hole horizons in the presence of strong, non-axisymmetric, gravitational waves (Brill waves). We have noticed that, in many cases, although the metric of the horizon seems to have large deviations from axisymmetry, the intrinsic geometry of the horizon is almost axisymmetric. The origin of the large apparent non-axisymmetry of the metric is the deformation of the coordinate system in which the metric was computed.
Alcubierre Miguel
Bondarescu Mihai
Seidel Edward
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