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Vacuum Boundary Problem of the Metric Produced by Perfect Fluid Mass Distributions Makino, Tetu
Description
The mathematical study of the metric produced by compactly supported perfect fluid mass distributions governed by the Einstein-Euler equations is now developing. The main difficulty of the study comes from the situation that the boundary between the mass and the vacuum requires mathematically delicate treatise. This so called `physical vacuum boundary' is a kind of free boundary. The spherically symmetric evolution of the metric near spherically symmetric equilibria, say, solutions of the Tolman-Oppenheimer-Volkoff equation, is studied in [1] by application of the Nash-Moser theorem. The metric can be matched to the exterior Schwarrzschild metric in the vacuum region, but it turns out to be the boundary is of class C^2 if and only if the metric is static. The existence of the axially symmetric metric of slowly rotating mass under the weak gravitational field has been established in [2] in a bonded region containing the support of the density. But the global continuation of the metric beyond the bounded region has not yet been done. Actually we are not sure whether the matching can be done using the Kerr metric, and, what on earth, we are not sure whether the metric can be continued as asymptotically flat one or not. Much less the problem of time evolution near this rotating stationary metric is completely open. [1] T. Makino, Kyoto J. Math., 56 (2016), 243-282. DOI 10.1215/21562261-3478880. [2] T. Makino, J. Math. Physics., 59(2018), 102502. DOI 10.1063/1.5026133.
Item Metadata
Title |
Vacuum Boundary Problem of the Metric Produced by Perfect Fluid Mass Distributions
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-07-31T09:05
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Description |
The mathematical study of the metric produced by compactly supported
perfect fluid mass distributions governed by the Einstein-Euler
equations is now developing. The main difficulty of the study comes from
the situation that the boundary between the mass and the vacuum requires
mathematically delicate treatise. This so called `physical vacuum
boundary' is a kind of free boundary. The spherically symmetric
evolution of the metric near spherically symmetric equilibria, say,
solutions of the Tolman-Oppenheimer-Volkoff equation, is studied in [1]
by application of the Nash-Moser theorem. The metric can be matched to
the exterior Schwarrzschild metric in the vacuum region, but it turns
out to be the boundary is of class C^2 if and only if the metric is
static. The existence of the axially symmetric metric of slowly rotating
mass under the weak gravitational field has been established in [2] in a
bonded region containing the support of the density. But the global
continuation of the metric beyond the bounded region has not yet been
done. Actually we are not sure whether the matching can be done using
the Kerr metric, and, what on earth, we are not sure whether the metric
can be continued as asymptotically flat one or not. Much less the
problem of time evolution near this rotating stationary metric is completely open.
[1] T. Makino, Kyoto J. Math., 56 (2016), 243-282. DOI
10.1215/21562261-3478880.
[2] T. Makino, J. Math. Physics., 59(2018), 102502. DOI
10.1063/1.5026133.
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Extent |
53.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Yamaguchi University
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Series | |
Date Available |
2020-01-28
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0388446
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International