Morawetz estimate for linearized gravity in Schwarzschild

Andersson, Lars; Blue, Pieter; Wang, Jinhua

doi:10.1007/s00023-020-00886-5

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Morawetz estimate for linearized gravity in Schwarzschild

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Andersson, Lars
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1708.06943.pdf
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引用

Andersson, L., Blue, P., & Wang, J. (2020). Morawetz estimate for linearized gravity in Schwarzschild. Annales Henri Poincaré, 21(3), 761-813. doi:10.1007/s00023-020-00886-5.

引用: https://hdl.handle.net/21.11116/0000-0003-587F-D

要旨

The equations governing the perturbations of the Schwarzschild metric satisfy
the Regge-Wheeler-Zerilli-Moncrief system. Applying the technique introduced in
[2], we prove an integrated local energy decay estimate for both the
Regge-Wheeler and Zerilli equations. In these proofs, we use some constants
that are computed numerically. Furthermore, we make use of the $r^p$ hierarchy
estimates [13, 32] to prove that both the Regge-Wheeler and Zerilli variables
decay as $t^{-\frac{3}{2}}$ in fixed regions of $r$.