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  Linear perturbations for the vacuum axisymmetric Einstein equations

Dain, S., & Reiris, M. (2011). Linear perturbations for the vacuum axisymmetric Einstein equations. Annales Henri Poincare, 12, 49-65. doi:10.1007/s00023-010-0074-z.

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1005.5347 (Preprint), 208KB
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 Creators:
Dain, Sergio, Author
Reiris, Martin1, Author           
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
 Abstract: In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in the global evolution. In this gauge the equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. Due to the rather peculiar properties of the system, the local in time existence has proved to resist analysis by standard methods. To analyze the principal part of the equations, which may represent the main source of the difficulties, we study linear perturbation around the flat Minkowski solution in this gauge. In this article we solve this linearized system explicitly in terms of integral transformations in a remarkable simple form. This representation is well suited to obtain useful estimates to apply in the non-linear case.

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 Dates: 2010-05-282010-07-282011
 Publication Status: Issued
 Pages: 13 pages. We suppressed the statements about decay at infinity. The proofs of these statements were incomplete. The complete proofs will require extensive technical analysis. We will studied this in a subsequent work. We also have rewritten the introduction and slighted changed the title
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Title: Annales Henri Poincare
Source Genre: Journal
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Publ. Info: Basel : Birkha.user
Pages: - Volume / Issue: 12 Sequence Number: - Start / End Page: 49 - 65 Identifier: ISSN: 1424-0637
CoNE: https://pure.mpg.de/cone/journals/resource/954925494977_2