Making use of geometrical invariants in black hole collisions

Abstract

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 {\sl 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 perturbative dynamics provide an accurate estimate of the radiation waveform and energy. This makes $\mathcal{S}$ particularly suited to studying the transition from nonlinear to linear dynamics and for invariant interpretation of numerical results.

arXiv comment4 pages, 3 eps figures, Revtex

References in corpus (12)

• Colliding Black Holes: The Close Limit
• Second order gauge invariant gravitational perturbations of a Kerr black hole
• Mechanics of Isolated Horizons
• Colliding black holes: how far can the close approximation go?
• Head-on collision of two black holes: comparison of different approaches
• The collision of boosted black holes
• Gravitational waves from black hole collisions via an eclectic approach
• The collision of boosted black holes: second order close limit calculations
• Calculation of gravitational wave forms from black hole collisions and disk collapse: Applying perturbation theory to numerical spacetimes
• The imposition of Cauchy data to the Teukolsky equation III: The rotating case
• The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
• The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations

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