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Static vacuum spacetimes with one compact dimension include black holes with localized horizons but also uniform and nonuniform black strings where the horizon wraps over the compact dimension. We present new numerical solutions for these localized black holes in 5 and 6 dimensions. Combined with previous 6D nonuniform string results, these provide evidence that the black hole and nonuniform string branches join at a topology changing solution.
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Kudoh et al. (2005) studied this question.
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