Decay of solutions to the Maxwell equation on the Schwarzschild background. (29th March 2016)

• Record Type: Journal Article
• Authors: Andersson, Lars; Bäckdahl, Thomas; Blue, Pieter
• Is Part Of: Classical and quantum gravity. Volume 33:Number 8(2016:Apr.)
• Publication Date: 2016-03-29
• Subjects: Maxwell equation -- Schwarzschild -- energy estimate -- Morawetz estimate; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/8/085010
• Languages: English
• ISSNs: 0264-9381

Abstract

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 defined in terms of the Maxwell field and its first derivatives. The superenergy tensor, although not conserved, yields a conserved higher order energy current . The tensor 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.