Abstract
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 $\kappa =\pm 1,\pm 2,...$. The problem is formulated as a harmonic map of Riemannian manifolds in which the integer $\kappa $ equals to the degree of the map.
Highlights
The topic of metrical kinks has a long history in general relativity [1,2,3,4,5,6,7,8] which declined recently toward oblivion
In conclusion we comment that the topological properties of field theory were well defined in a flat space background
Due to the singular and non-compact manifolds of general relativity these concepts found no simple applications in a curved spacetime
Summary
The topic of metrical kinks has a long history in general relativity [1,2,3,4,5,6,7,8] which declined recently toward oblivion. These emerge mostly in flat 3+1-dimensional spacetime, with the advent of higher/lower dimensions the same topological concepts may find applications in these cases as well
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