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A new method to compute quasi-local spin and other invariants on marginally trapped surfaces

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Jasiulek,  Michael
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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0906.1228v1.pdf
(Preprint), 2MB

CQG_26_24_245008.pdf
(Any fulltext), 811KB

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Citation

Jasiulek, M. (2009). A new method to compute quasi-local spin and other invariants on marginally trapped surfaces. Classical and quantum gravity, 26(24): 245008. doi:10.1088/0264-9381/26/24/245008.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-6084-5
Abstract
We accurately compute the scalar 2-curvature, the Weyl scalars, associated quasi-local spin, mass and higher multipole moments on marginally trapped surfaces in numerical 3+1 simulations. To determine the quasi-local quantities we introduce a new method which requires a set of invariant surface integrals, allowing for surface grids of a few hundred points only. The new technique circumvents solving the Killing equation and is also an alternative to approximate Killing vector fields. We apply the method to a perturbed black hole ringing down to Kerr and compare the quasi-local spin with other methods that use Killing vector fields, coordinate vector fields, quasinormal ringing and properties of the Kerr metric on the surface. It even agrees with the spin of approximate Killing vector fields during the phase of perturbed axisymmetry. Additionally, we introduce a new coordinate transformation, adapting spherical coordinates to any two points on the sphere like the two minima of the scalar 2-curvature on axisymmetric trapped surfaces.