# 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.

Zeitschrift:
Class. Quantum Grav.
Verlag:
IOP Publishing
Seiten:
085010
Band:
33, no. 8

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