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Static axisymmetric spacetimes with prescribed multipole moments
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2005 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 22, no 9, 1607-1621 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we develop a method of finding the static axisymmetric spacetime corresponding to any given set ofmultipolemoments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static spacetime for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernández-Pastora and Martín concerning the monopole–quadrupole solution.

Place, publisher, year, edition, pages
2005. Vol. 22, no 9, 1607-1621 p.
Keyword [en]
static, axisymmetric, exact solution, multipole moments, spacetime, algebraic equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-13749DOI: 10.1088/0264-9381/22/9/009OAI: oai:DiVA.org:liu-13749DiVA: diva2:21291
Available from: 2006-01-12 Created: 2006-01-12 Last updated: 2009-05-07
In thesis
1. Multipole Moments of Stationary Spacetimes
Open this publication in new window or tab >>Multipole Moments of Stationary Spacetimes
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study the relativistic multipole moments for stationary asymptotically flat spacetimes as introduced by Geroch and Hansen. These multipole moments give an asymptotic description of the gravitational field in a coordinate independent way.

Due to this good description of the spacetimes, it is natural to try to construct a spacetime from only the set of multipole moments. Here we present a simple method to do this for the static axisymmetric case. We also give explicit solutions for the cases where the number of non-zero multipole moments are finite. In addition, for the general stationary axisymmetric case, we present methods to generate solutions.

It has been a long standing conjecture that the multipole moments give a complete characterization of the stationary spacetimes. Much progress toward a proof has been made over the years. However, there is one remaining difficult task: to prove that a spacetime exists with an a-priori given arbitrary set of multipole moments subject to some given condition.

Here we present such a condition for the axisymmetric case, and prove that it is both necessary and sufficient. We also extend this condition to the general case without axisymmetry, but in this case we only prove the necessity of our condition.

Place, publisher, year, edition, pages
Matematiska institutionen, 2008. 18 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1181
Keyword
multipole moments, stationary, static, relativistic, spacetime, convergence, specified
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-11519 (URN)978-91-7393-902-7 (ISBN)
Public defence
2008-08-22, Planck, Fysikhuset, Campus Valla, Linköpings universitet, Linköpings universitet, 10:15 (English)
Opponent
Supervisors
Available from: 2008-05-21 Created: 2008-05-21 Last updated: 2009-04-24
2. Multipole moments of axisymmetric spacetimes
Open this publication in new window or tab >>Multipole moments of axisymmetric spacetimes
2006 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study multipole moments of axisymmetric spacetimes. Using the recursive definition of the multipole moments of Geroch and Hansen we develop a method for computing all multipole moments of a stationary axisymmetric spacetime without the use of a recursion. This is a generalisation of a method developed by Herberthson for the static case.

Using Herberthson’s method we also develop a method for finding a static axisymmetric spacetime with arbitrary prescribed multipole moments, subject to a specified convergence criteria. This method has, in general, a step where one has to find an explicit expression for an implicitly defined function. However, if the number of multipole moments are finite we give an explicit expression in terms of power series.

Place, publisher, year, edition, pages
Matematiska institutionen, 2006. 46 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1223
Keyword
multipole moments, axisymmetry, spacetimes, prescribed, solutions, static, stationary, Kerr, Weyl, Ernst
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-5400 (URN)91-85457-98-1 (ISBN)
Presentation
2006-01-30, BL32, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Note
Note: The two articles are also available in the pdf-file. Report code: LiU-TEK-LIC-2006:4.Available from: 2006-01-12 Created: 2006-01-12 Last updated: 2009-05-07

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Bäckdahl, ThomasHerberthson, Magnus

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