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
non-axisymmetric 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.
Interesting is the agreement 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.Comment: 22 pages, 5 figure
