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

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<strong>Numerical</strong> Experiments - Convergence· s = −2, a = 0.9, l ′ = 2, ID0Log 10 ckLog 10 ck051015202530T⩵0.350 20 40 60 80 100k051015202530T⩵409.338350 20 40 60 80 100kLog 10 ckLog 10 ck051015202530T⩵49.1205350 20 40 60 80 100k051015202530T⩵1473.62350 20 40 60 80 100k· at late times <strong>solution</strong> can be described by few modes16 / 20
Conclusion - Formulas for s ≠ 0 with ID0 and ID2· at R + :{µ l =l 0 + l + 3 + b −1 for l ′ = l 0 , l 0 + 1l ′ + l + 2 + b −1 for l ′ > l 0 + 1· at ˜R:{µ l =l 0 + l + 3 −1 for l ′ = l 0 , l 0 + 1l ′ + l + 2 −1 for l ′ > l 0 + 1· at J + :⎧⎨ l − s + 2 −1 for l ′ = l 0 , l 0 + 1µ l = l ′ − s + 1 −1⎩l − s + 2 −1for l ′ > l 0 + 1 and l < l ′for l ′ > l 0 + 1 and l ≥ l ′, where l 0 = max(|s|, |m|) is <strong>the</strong> lowest excitable modeand b = 0 in general but b = 1 for <strong>the</strong> special case s > 0, m = 017 / 20
Page 1 and 2: Numerical Solution
Page 3 and 4: The Teukolsky Equa
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 13 and 14: Numerical Experime
Page 15: Numerical Experime
Page 19 and 20: Conclusion· new formulation <stron

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