liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Axisymmetric stationary solutions with arbitrary multipole moments
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2007 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 24, no 9, 2205-2215 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments is studied. The condition on the multipole moments, for the existence of a solution, is formulated as a convergence condition on a power series formed from the multipole moments. The methods in this paper can also be used to give approximate solutions to any order, as well as estimates on each term of the resulting power series.

Place, publisher, year, edition, pages
2007. Vol. 24, no 9, 2205-2215 p.
Keyword [en]
multipole moments, statinary, axisymmetric, existence, spacetime
National Category
URN: urn:nbn:se:liu:diva-13159DOI: 10.1088/0264-9381/24/9/004OAI: diva2:17944
Available from: 2008-05-21 Created: 2008-05-21 Last updated: 2009-04-24
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.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1181
multipole moments, stationary, static, relativistic, spacetime, convergence, specified
National Category
Other Physics Topics
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)
Available from: 2008-05-21 Created: 2008-05-21 Last updated: 2009-04-24

Open Access in DiVA

No full text

Other links

Publisher's full textLink to Ph.D. Thesis

Search in DiVA

By author/editor
Bäckdahl, Thomas
By organisation
Applied MathematicsThe Institute of Technology

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 386 hits
ReferencesLink to record
Permanent link

Direct link