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キーワード:
Mathematics, Analysis of PDEs, math.AP,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
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 $r$.
