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Spectral method for metric perturbations of black holes: Kerr background case in general relativity
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abstract
We present a novel approach, $\textit{Metric pErTuRbations wIth speCtral methodS}$ (METRICS), to calculate the gravitational metric perturbations and the quasinormal-mode frequencies of rotating black holes of any spin without decoupling the linearized field equations. We demonstrate the method by applying it to perturbations of Kerr black holes of any spin, simultaneously solving all ten linearized Einstein equations in the Regge-Wheeler gauge through purely algebraic methods and computing the fundamental (co-rotating) quadrupole mode frequency at various spins. We moreover show that the METRICS approach is accurate and precise, yielding (i) quasinormal mode frequencies that agree with Leaver's, continuous-fraction solution with a relative fractional error smaller than $10^{-5}$ for all dimensionless spins below up to 0.95, and (ii) metric perturbations that lead to Teukolsky functions that also agree with Leaver's solution with mismatches below $1\%$ for all spins below 0.9. By not requiring the decoupling or the angular separation of the linearized field equations, the METRICS approach has the potential to be straightforwardly adapted for the computation of the quasinormal-mode frequencies of rotating black holes of any spin beyond general relativity or in the presence of matter.
Forward citations
Cited by 6 Pith papers
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A derivation is presented that separates the linearized Einstein equations in Kerr spacetime and expresses all metric perturbation components in terms of Teukolsky master functions.
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Explicit infinite family of axisymmetric black holes with a Kerr exterior, a regular or mildly singular interior controlled by free exponents n_i, and no additional asymptotic charges.
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Spacetime of rotating black holes surrounded by massive scalar charges
Spectral methods construct leading-order spinning black-hole spacetimes with massive scalar hair for spin a≤0.8 and scalar mass µ≤0.2/M.
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Computing spectral shifts for Johannsen-Psaltis black holes
Slowly rotating Johannsen–Psaltis black holes have definite-parity quasinormal modes with even/odd frequency shifts split by the deviation parameter, computed here through ℓ=10.
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