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Optimal decay for solutions of the Teukolsky equation on the Kerr metric for the full subextremal range |a| < M
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abstract
We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term (predicted by Price's law) in the large time regime assuming that the initial data have compact support and have enough (but finite) Sobolev regularity. For initial data with less spatial decay (typically decaying like r^{--1--$\alpha$} with $\alpha$ $\in$ (0, 1)), we prove that the solution has a pointwise decay of order t^{--1--$\alpha$--s--|s|+} on spatially compact regions. In the proof, we adopt the spectral point of view and make use of recent advances in microlocal analysis and non elliptic Fredholm theory which provide a robust framework to study linear operators on black hole type spacetimes.
Forward citations
Cited by 5 Pith papers
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Linear stability of Kerr black holes in the full subextremal range
Proof that linearized perturbations of subextremal Kerr black holes decay to a linearized Kerr solution for the full range |a| < m.
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Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range $|a|<M$
For all sub-extremal Kerr spacetimes |a|<M, angular elliptic estimates control the full linearised curvature by the extremal Teukolsky components up to lower-order terms.
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The Teukolsky scalar as a gateway for quantizing gravity on rotating black holes
A Hadamard Unruh state is claimed for quantized Teukolsky scalars on subextreme Kerr, using an enlarged hermitian Green-hyperbolic operator.
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A Physical space derivation of Morawetz-Energy estimates in Kerr spacetimes with large angular momentum
Physical-space Morawetz-energy estimates hold for the scalar wave equation on Kerr with |a|/m ≤ 0.75, via trapping-set characterization, Stogin-type low-frequency control, and a physical-space Whiting transform.
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Teukolsky on slowly-rotating Kerr-de Sitter in the vanishing $\Lambda$ limit
Energy, Morawetz and r^p-weighted estimates are proved for Teukolsky equations on slowly-rotating Kerr-de Sitter, uniformly as the cosmological constant tends to zero, recovering known Kerr-Teukolsky estimates in the limit.
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