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Decay of solutions to the Maxwell equation on the Schwarzschild background

Andersson, L., Bäckdahl, T., & Blue, P. (2016). Decay of solutions to the Maxwell equation on the Schwarzschild background. Classical and Quantum Gravity, 33(8): 085010. doi:10.1088/0264-9381/33/8/085010.

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Creators:
Bäckdahl, Thomas1, Author
Blue, Pieter, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012

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Free keywords: 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.

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Dates: 2015-01-1920152016
Publication Status: Published in print
Pages: 14 pages
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1501.04641
DOI: 10.1088/0264-9381/33/8/085010
Degree: -

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Title: Classical and Quantum Gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 33 (8) Sequence Number: 085010 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1