Decay of solutions to the Maxwell equation on the Schwarzschild background
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Classical and Quantum Gravity 33 (8): 085010+ (Apr 21, 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.
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