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We describe static, brane--like, solutions to vacuum Einstein's equations inD = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutionshave positive ADM mass but no horizon. The curvature invariants are finiteeverywhere except at r = 0 where r is the radial coordinate in the m + 1dimensional space. The presence of n \ge 1 extra dimensions is crucial forthese properties. Such solutions may be naturally anticipated if Mathur'sfuzzball proposal for black holes is correct.

Static brane--like vacuum solutions in D \ge 5 dimensional spacetime with positive ADM mass but no horizon