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Mathematics, Analysis of PDEs, math.AP,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,
Abstract:
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 on the Schwarzschild exterior to the Coulomb solution.
