Abstract
Static, axisymmetric, vacuum metrics (commonly called Weyl metrics) are classified according to the homothetic motions they admit, with all having more than two homothetic motions explicitly computed. Within the two new families of spacetimes so determined, none of the metrics is asymptotically flat. Although most of the horizons are unlike that of the Schwarzschild metric, it is shown that they nonetheless all fall within a classification scheme previously developed for two-dimensional static metrics. TheC — metric and the question of directional singularities are also briefly considered.
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