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Multipole moments of axisymmetric spacetimes
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
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 [en]
multipole moments, axisymmetry, spacetimes, prescribed, solutions, static, stationary, Kerr, Weyl, Ernst
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:liu:diva-5400ISBN: 91-85457-98-1 (print)OAI: oai:DiVA.org:liu-5400DiVA: diva2:21293
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
List of papers
1. Static axisymmetric spacetimes with prescribed multipole moments
Open this publication in new window or tab >>Static axisymmetric spacetimes with prescribed multipole moments
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.

Keyword
static, axisymmetric, exact solution, multipole moments, spacetime, algebraic equation
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-13749 (URN)10.1088/0264-9381/22/9/009 (DOI)
Available from: 2006-01-12 Created: 2006-01-12 Last updated: 2009-05-07
2. Explicit multipole moments of stationary axisymmetric spacetimes
Open this publication in new window or tab >>Explicit multipole moments of stationary axisymmetric spacetimes
2005 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 22, no 17, 3585-3594 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we study multipole moments of axisymmetric stationary asymptotically flat spacetimes. We show how the tensorial recursion of Geroch and Hansen can be reduced to a recursion of scalar functions. We also demonstrate how a careful choice of conformal factor collects all moments into one complex-valued function on , where the moments appear as the derivatives at 0. As an application, we calculate the moments of the Kerr solution. We also discuss the freedom in choosing the potential for the moments.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-13750 (URN)10.1088/0264-9381/22/17/017 (DOI)
Available from: 2006-01-12 Created: 2006-01-12 Last updated: 2009-02-16

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Bäckdahl, Thomas

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf