Decay of solutions to the Maxwell equation on the Schwarzschild background
Journal article, 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 derivative(t))(b). The tensor Hab 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.
spin
wave-equation
energy estimate
tensors
perturbations
manifolds
Maxwell equation
field
Morawetz estimate
Schwarzschild
geometry
rotating black hole
kerr spacetime
energy
Author
L. Andersson
Max Planck Society
Royal Institute of Technology (KTH)
Thomas Bäckdahl
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
P. Blue
University of Edinburgh
Classical and Quantum Gravity
0264-9381 (ISSN) 13616382 (eISSN)
Vol. 33 8 085010Subject Categories (SSIF 2011)
Physical Sciences
DOI
10.1088/0264-9381/33/8/085010