Mihai Bondarescu et al 2002 Class. Quantum Grav. 19 375 doi:10.1088/0264-9381/19/2/311
Mihai Bondarescu1, Miguel Alcubierre1 and Edward Seidel1,2
Show affiliationsThe 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 an embedding exists. Our method is based on expanding the surface in spherical harmonics and minimizing the differences between the metric on the original surface and on the trial surface in the space of the expansion coefficients. We have applied this method to study the geometry of black-hole horizons in the presence of strong, non-axisymmetric, gravitational waves (Brill waves). We have noted 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.
04.70.-s Physics of black holes
04.20.Gz Spacetime topology, causal structure, spinor structure
Issue 2 (21 January 2002)
Received 2 October 2001, in final form 21 November 2001
Published 2 January 2002
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