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

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Conclusion - Formulas for s ≠ 0 with ID1 and ID3· at R + :⎧⎨ l 0 + l + 3 + b −1 for l ′ = l 0µ l = l 0 + l + 4 + b −1 for l ′ = l 0 + 1⎩l ′ + l + 1 + b −1 for l ′ > l 0 + 1⎧⎨ l 0 + l + 3 −1 for l ′ = l 0· at ˜R:µ l = l 0 + l + 4 −1⎩l ′ + l + 1 −1for l ′ = l 0 + 1for l ′ > l 0 + 1· at J + :⎧l − s + 2 −1 for l ′ = l 0⎪⎨ l − s + 3 −1 for l ′ = l 0 + 1 and l = l 0µ l = l − s + 2 −1 for l ′ = l 0 + 1 and l > l 0l⎪⎩′ − s −1 for l ′ > l 0 + 1 and l < l ′ − 1l − s + 2 −1 for l ′ > l 0 + 1 and l ≥ l ′ − 1⇒ same decrement by 1 as for switch ID0 → ID218 / 20
Conclusion· new formulation <strong>of</strong> <strong>the</strong> TKEq in RT-foliation, which is regularover <strong>the</strong> whole domain, including R + and J +· conrmation <strong>of</strong> decay rates µ l <strong>of</strong> [RT, 2011] for s = 0· empirical formulas for µ l for s ≠ 0 with ID0,ID1,ID2,ID3· rst num. verication <strong>of</strong> LPI-split in space for s > 0, m = 0· discovered splitting <strong>of</strong> LPI in time for s ≠ 0Outlook· up to now only axisymmetric initial data m = 0,(superradiance experiments)· particle perturbation19 / 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 17: Conclusion - Formulas for s ≠ 0 w

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