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

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Our Approach· transform TKEq to Kerr-ingoing coors and apply hyperboloidalcompacticationτ = T + h(R)r =RΩ(R)· h height function, Ω compress function· we follow [Rácz, Tóth, 2011] (RT) choices for h and Ω⇒ smooth, horizon-penetrating, hyperboloidal foliation <strong>of</strong> Kerr i 0 i 0 Figure: Conformal SS diagram. τ -slices as blue, RT-slices as green solid lines.4 / 20
Coordinate Speeds in RT-FoliationIngoing and Outgoing coordinate speeds0.100.05M= 1, a = 0R 0.618c Rc±R0.000.05c R0.100.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00R· coordinate speeds vanish at R + respectively J +⇒ no boundary conditions needed5 / 20
Page 1 and 2: Numerical Solution
Page 3: The Teukolsky Equa
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

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

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