A topological metric in 2+1-dimensions

Real-valued triplet of scalar fields as source gives rise to a metric which tilts the scalar, not the light cone, in 2+1-dimensions. The topological metric is static, regular and it is characterized by an integer $κ=\pm 1,\pm 2,...$. The problem is formulated as a harmonic map of Riemannian manifolds in which the integer $κ$ equals to the degree of the map.

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