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Nonlinear Tails of Gravitational Waves in Schwarzschild Black Hole Ringdown
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abstract
Schwarzschild black holes evolve toward their static configuration by emitting gravitational waves, which decay over time following a power law at fixed spatial positions. We derive this power law analytically for the second-order even gravitational perturbations, demonstrating that it is determined by the fact that the second-order source decays as the inverse square of the distance. Quadratic gravitational modes with multipole $\ell$ decay according to a law $\sim t^{-2\ell-1}$, in contrast to the linear Price law scaling $\sim t^{-2\ell-3}$. Consequently, nonlinear tails may persist longer than their linear counterparts.
Forward citations
Cited by 3 Pith papers
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Nonlinearities in Kerr Black Hole Ringdown from the Penrose Limit
Kerr quadratic quasi-normal mode amplitudes and phases are computed analytically in the eikonal limit via the Penrose limit, giving an explicit spin-dependent nonlinearity ratio.
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The AdS Perspective on the Nonlinear Tails in Black Hole Ringdown
The known t^{-(2L+2)} nonlinear ringdown tail is rederived via AdS2 x S2, with a proposed but incorrectly normalized Aretakis amplitude relation.
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The Nonlinear Tails in Black Hole Ringdown: the Scattering Perspective
Nonlinear ringdown tails in the transverse-traceless gauge decay as t^{-(2ℓ+1)}, and this paper rederives that law from in-in scattering diagrams.
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