Making use of geometrical invariants in black hole collisions

We consider curvature invariants in the context of black hole collision simulations. In particular, we propose a simple and elegant combination of the Weyl invariants I and J, the speciality index $\mathcal{S}.$ In the context of black hole perturbations $\mathcal{S}$ provides a measure of the size of the distortions from an ideal Kerr black hole spacetime. Explicit calculations in well-known examples of axisymmetric black hole collisions demonstrate that this quantity may serve as a useful tool for predicting in which cases the close limit can provide an accurate estimate of the radiation wave form and energy. This makes $\mathcal{S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for an invariant interpretation of numerical results.