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Branched Spacetime Geometries from Harmonic $S^2$ Maps: Energy Matching and Its Limitations
We investigate a topological construction of general-relativistic geometries based on harmonic self-maps of the two-sphere, $S^{2}\rightarrow S^{2}$. Such maps are classified by an integer degree $k$. For $k>1$, however, the pullback angular metric is not globally smooth: it defines a branched cover
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