Decay of solutions to the Maxwell equation on the Schwarzschild background

Autoren: Lars Andersson, Thomas Bäckdahl, Pieter Blue (2016)

A new Morawetz or integrated local energy decay estimate for Maxwell test fields on the exterior of a Schwarzschild black hole spacetime is proved. The proof makes use of a new superenergy tensor $H_{ab}$ defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current $H_{ab}(\partial_t)^ b$. The tensor $H_{ab}$ vanishes for the static Coulomb field, and the Morawetz estimate proved here therefore yields integrated decay for the Maxwell field to the Coulomb solution on the Schwarzschild exterior.

Class. Quantum Grav.
IOP Publishing
33, no. 8

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