Stationary vacuum hyper-cylindrical solution in 4+1 dimensions

摘要

We find a 4+1 dimensional stationary vacuum hyper-cylindrical solutionsolution which is spherically symmetric in $3-$dimensions and invariant underthe translation along the fifth coordinate. The solution is characterized bythree parameters, mass, tension, and conserved momentum along the fifthcoordinate. The metric is locally equivalent to the known static solution. Webriefly discuss its physical properties.