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arXiv · 1708.06943

Morawetz estimate for linearized gravity in Schwarzschild

Lars Andersson·Pieter Blue·Jinhua Wang
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Abstract

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 $r$.

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Lars Andersson, Pieter Blue, Jinhua Wang. 2017-08-23. Morawetz estimate for linearized gravity in Schwarzschild. https://arxiv.org/abs/1708.06943

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