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Journal Article

Linear perturbations for the vacuum axisymmetric Einstein equations

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons26309

Reiris,  Martin
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1005.5347
(Preprint), 208KB

AHP12_49.pdf
(Any fulltext), 246KB

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There is no public supplementary material available
Citation

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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-107C-C
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.