Static Solution of the General Relativistic Nonlinear $σ$-Model Equation

Details Static Solution of the General Relativistic Nonlinear $σ$-Model Equation Static Solution of the General Relativistic Nonlinear $σ$-Model Equation

1994-07-14

arxiv.org/abs/hep-th/9407072v1

Phys.Rev.D50:4219-4222,1994

Physics

High Energy Physics

High Energy Physics - Theory

ReVTeX 10 pages, 2 figures automatically included, uuencoded, HYUPT-93/08

Scientific paper

10.1103/PhysRevD.50.4219

The nonlinear $\sigma$-model is considered to be useful in describing hadrons (Skyrmions) in low energy hadron physics and the approximate behavior of the global texture. Here we investigate the properties of the static solution of the nonlinear $\sigma$-model equation coupled with gravity. As in the case where gravity is ignored, there is still no scale parameter that determines the size of the static solution and the winding number of the solution is $1/2$. The geometry of the spatial hyperspace in the asymptotic region of large $r$ is explicitly shown to be that of a flat space with some missing solid angle.

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