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  A flow approach to Bartnik's static metric extension conjecture in axisymmetry

Cederbaum, C., Rinne, O., & Strehlau, M. (2019). A flow approach to Bartnik's static metric extension conjecture in axisymmetry. Pure and Applied Mathematics Quarterly, 15(2), 611-666. doi:10.4310/PAMQ.2019.v15.n2.a1.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0003-AD8A-F Version Permalink: http://hdl.handle.net/21.11116/0000-0005-51F4-C
Genre: Journal Article

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1904.11040.pdf (Preprint), 632KB
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 Creators:
Cederbaum, Carla, Author
Rinne, Oliver1, Author              
Strehlau, Markus1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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Free keywords: Mathematics, Differential Geometry, math.DG,General Relativity and Quantum Cosmology, gr-qc
 Abstract: We investigate Bartnik's static metric extension conjecture under the additional assumption of axisymmetry of both the given Bartnik data and the desired static extensions. To do so, we suggest a geometric flow approach, coupled to the Weyl-Papapetrou formalism for axisymmetric static solutions to the Einstein vacuum equations. The elliptic Weyl-Papapetrou system becomes a free boundary value problem in our approach. We study this new flow and the coupled flow--free boundary value problem numerically and find axisymmetric static extensions for axisymmetric Bartnik data in many situations, including near round spheres in spatial Schwarzschild of positive mass.

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 Dates: 2019-04-24201920192019
 Publication Status: Published in print
 Pages: 57 pages, 13 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1904.11040
URI: http://arxiv.org/abs/1904.11040
DOI: 10.4310/PAMQ.2019.v15.n2.a1
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Title: Pure and Applied Mathematics Quarterly
Source Genre: Journal
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Pages: - Volume / Issue: 15 (2) Sequence Number: - Start / End Page: 611 - 666 Identifier: -