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.