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arXiv · 2206.02193

Peeling for tensorial wave equations on Schwarzschild spacetime

Pham Truong Xuan
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Abstract

In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-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 $\mathscr{I}^\pm$ and the initial Cauchy hypersurface $\Sigma_0 = \left\{ t=0 \right\}$ in a neighbourhood 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.

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Pham Truong Xuan. 2022-06-05. Peeling for tensorial wave equations on Schwarzschild spacetime. https://doi.org/10.1142/s0129055x2350023x

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