Numerical solution of the 2+1 Teukolsky equation on a ...

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Goal· accurate numerical <strong>solution</strong> <strong>of</strong> <strong>the</strong> <strong>Teukolsky</strong> Equation in <strong>the</strong>time domain· application on <strong>the</strong> late time decay (tails) <strong>of</strong> generic spin weightperturbationsStructure <strong>of</strong> <strong>the</strong> Talk1. The <strong>Teukolsky</strong> Equation2. The Hyperboloidal Approach3. Pseudo-Spectral and FD-Evolution-Codes4. <strong>Numerical</strong> Experiments5. Conclusion2 / 20
The <strong>Teukolsky</strong> Equation, hereafter TKEq, [<strong>Teukolsky</strong>, 1973]· derived originally in Boyer-Lindquist coordinates· describes <strong>the</strong> evolution <strong>of</strong> linear perturbations <strong>of</strong> a rotatingblack hole (Kerr BH with mass M, spec. angular momentum a)· a wavelike <strong>equation</strong> for <strong>the</strong> eld variable ΨType <strong>of</strong> perturbation depends on spin weight parameter s· Ψ refers to dierent elds depending on s,e.g. for s = −2 it is Ψ = (r − i cos θ) 4 · Ψ 4· for s = 0 <strong>the</strong> TKEq is just <strong>the</strong> 3D scalar wave <strong>equation</strong> onKerr□Ψ = 03 / 20
Page 1: Numerical Solution
Page 5 and 6: Coordinate Speeds in RT-FoliationIn
Page 7 and 8: ImplementationPseudo-spectral-evolu
Page 9 and 10: Qualitative Evolution of</s
Page 11 and 12: Numerical Experime
Page 17 and 18: Conclusion - Formulas for s ≠ 0 w
Page 19 and 20: Conclusion· new formulation <stron

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