On the T-3-Gowdy symmetric Einstein-Maxwell equations
2006 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 7, no 1, 1-20 p.Article in journal (Refereed) Published
Recently, progress has been made in the analysis of the expanding direction of Gowdy spacetimes. The purpose of the present paper is to point out that some of the techniques used in the analysis can be applied to other problems. The essential equations in the case of the Gowdy spacetimes can be considered as a special case of a wider class of variational problems. Here we are interested in the asymptotic behaviour of solutions to this class of equations. Two particular members arise when considering the T-3-Gowdy symmetric Einstein-Maxwell equations and when considering T-3-Gowdy symmetric IIB superstring cosmology. The main result concerns the rate of decay of a naturally defined energy. A subclass of the variational problems can be interpreted as wave map equations, and in that case one gets the following picture. The non-linear wave equations one ends up with have as a domain the positive real line in Cartesian product with the circle. For each point in time, the wave map can thus be seen as a loop in some Riemannian manifold. As a consequence of the decay of the energy mentioned above, the length of the loop converges to zero at a specific rate.
Place, publisher, year, edition, pages
2006. Vol. 7, no 1, 1-20 p.
IdentifiersURN: urn:nbn:se:kth:diva-15436DOI: 10.1007/s00023-005-0239-3ISI: 000235450100001ScopusID: 2-s2.0-33644891030OAI: oai:DiVA.org:kth-15436DiVA: diva2:333477
QC 201005252010-08-052010-08-05Bibliographically approved