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Calculation of, and bounds for, the multipole moments of stationary spacetimes
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.
2006 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 23, no 20, 5997-6006 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the multipole moments of stationary asymptotically flat spacetimes are considered. We show how the tensorial recursion of Geroch and Hansen can be replaced by a scalar recursion on . We also give a bound on the multipole moments. This gives a proof of the 'necessary part' of a long-standing conjecture due to Geroch.

Place, publisher, year, edition, pages
2006. Vol. 23, no 20, 5997-6006 p.
Keyword [en]
multipole moments, stationary, spacetimes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-13158DOI: 10.1088/0264-9381/23/20/019OAI: oai:DiVA.org:liu-13158DiVA: diva2:17943
Available from: 2008-05-21 Created: 2008-05-21 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

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Bäckdahl, ThomasHerberthson, Magnus

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