2017-04-06 14:00 — 15:00
Middle Lecture Room, Math Building
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.