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

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TKEq on RT-FoliationThe eld variable needs rescaling· RT rescaling: Ψ → r −1 Ψ· enough for s = 0, but singular at R + for s ≠ 0⇒ simple proposal:· where ∆ = r 2 − 2Mr + a 2Ψ → ∆ −s · r −1 Ψ· this rescaling yields a new formulation <strong>of</strong> <strong>the</strong> TKEq, which isregular over <strong>the</strong> whole domain [R + , J + ]6 / 20
ImplementationPseudo-spectral-evolution-code = PS-code· Method <strong>of</strong> Lines, RK4-time integrator· derivative approximation by· Chebyshev in radial direction (Gauss-Lobatto-grid)· Fourier in angular direction (staggered grid)· quadruple-precision possibleFinite-dierencing-evolution-code = FD-code· basically <strong>the</strong> same but:· equidistant grid in radial direction· derivatives with FD stencils(up to 6th order, lop-sided near and sided at boundaries)(Note: exploiting axisymmetry we implemented <strong>the</strong> TKEq in 2 + 1 )7 / 20
Page 1 and 2: Numerical Solution
Page 3 and 4: The Teukolsky Equa
Page 5: Coordinate Speeds in RT-FoliationIn
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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