Morawetz estimate for linearized gravity in Schwarzschild

2017/08/23 by Andersson, Lars, Blue, Pieter, Wang, Jinhua
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1708.06943

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^-(3)/(2) in fixed regions of r.

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