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- W2950466799 abstract "We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$ for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the Regge-Wheeler tortoise coordinate is large, $r_*>epsilon t$, we obtain decay for the null components with rates of $|phi_+| sim |alpha| < C r^{-5/2}$, $|phi_0| sim |rho| + |sigma| < C r^{-2} |t-r_*|^{-1/2}$, and $|phi_{-1}| sim |underline{alpha}| < C r^{-1} |t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$, and when $t+r_*1$, all components (normalized with respect to an ingoing null basis) decay at a rate of $C uout^{-1}$ with $uout=t+r_*$ in the exterior region." @default.
- W2950466799 created "2019-06-27" @default.
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- W2950466799 date "2007-10-22" @default.
- W2950466799 modified "2023-09-25" @default.
- W2950466799 title "Decay of the Maxwell field on the Schwarzschild manifold" @default.
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