Research PaperNo Access

Peeling for tensorial wave equations on Schwarzschild spacetime

Truong Xuan Pham

Faculty of Pedagogy, VNU University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

E-mail Address: [email protected]

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https://doi.org/10.1142/S0129055X2350023XCited by:1 (Source: Crossref)

Abstract

In this paper, we establish the asymptotic behavior along outgoing and incoming radial geodesics, i.e. the peeling property for the tensorial Fackerell–Ipser and spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method combines a conformal compactification with vector field techniques to prove the two-side estimates of the energies of tensorial fields through the future and past null infinity $ℐ^{\pm}$ and the initial Cauchy hypersurface $Σ_{0} = {t = 0}$ in a neighborhood of spacelike infinity $i_{0}$ far away from the horizon and future timelike infinity. Our results obtain the optimal initial data which guarantees the peeling at all orders.

Keywords:

AMSC: 35L05, 35P25, 35Q75, 83C57

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