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Decay of solutions to the Maxwell equation on the Schwarzschild background
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Albert Einstein Institute, Germany.
2016 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 33, no 8, 085010Article in journal (Refereed) Published
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Text
Abstract [en]

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

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2016. Vol. 33, no 8, 085010
Keyword [en]
energy estimate, Maxwell equation, Morawetz estimate, Schwarzschild
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-187209DOI: 10.1088/0264-9381/33/8/085010ISI: 000374832400010Scopus ID: 2-s2.0-84963799789OAI: oai:DiVA.org:kth-187209DiVA: diva2:929431
Note

QC 20160518

Available from: 2016-05-18 Created: 2016-05-18 Last updated: 2016-11-29Bibliographically approved

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