Are there static texture?

Details Are there static texture? Are there static texture?

1999-01-04

arxiv.org/abs/astro-ph/9901024v1

Phys.Rev.D59:125007,1999

Astronomy and Astrophysics

Astrophysics

12 page Latex file, 1 postscript figure, submitted to PRD

Scientific paper

10.1103/PhysRevD.59.125007

We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is defined. We investigate whether static solutions with non-trivial winding number exist. The answer which we can proof here is only partial: We show that within a certain family of maps no static solutions with non-zero winding number exist. We discuss the existing static solutions in our family of maps. An extension to other maps or a proof that our family of maps is sufficiently general remains an open problem.

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