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

Cederbaum, C., Rinne, O., & Strehlau, M. (in press). A flow approach to Bartnik's static metric extension conjecture in axisymmetry. Pure and Applied Mathematics Quarterly. Retrieved from http://arxiv.org/abs/1904.11040.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0003-AD8A-F Version Permalink: https://hdl.handle.net/21.11116/0000-0004-8FF4-8
Genre: Journal Article

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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: 2019-04-2420192019
 Publication Status: Accepted / In Press
 Pages: 57 pages, 13 figures
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1904.11040
URI: http://arxiv.org/abs/1904.11040
 Degree: -

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Title: Pure and Applied Mathematics Quarterly
Source Genre: Journal
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