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Morawetz Estimate for Linearized Gravity in the Schwarzschild Spacetime

Speaker

Jinhua Wang, Xiamen University

Time

2017.04.06 14:00-15:00

Venue

Middle Lecture Room, Math Building

Abstract

The equations governing the perturbations of the Schwarzschild metric satisfying the Regge-Wheeler (odd parities) and Zerilli equations (even parities). We prove the energy boundedness, the integrated local energy decay estimate and pointwise decay estimate for both Regge-Wheeler and Zerilli equations. This gives another proof for the linear stability of Schwarzschild metrics. Besides, analysis of symmetry operators yields transformations between Regge-Wheeler and Teukolsky variables. We show that confined to a class of data set, this transformation defines an isomorphism between the Regge-Wheeler and Teukolsky variables, and the decay for Teukolsky varialbe follows from that of Regge-Wheeler variable.