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 Institute

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)

Vol. 33 8

Subject Categories

Physical Sciences

DOI

10.1088/0264-9381/33/8/085010

More information

Latest update

2/28/2018