On a class of rotating gravitational waves

A class of solutions of the gravitational field equations describing vacuum spacetimes outside rotating cylindrical sources is presented. The spacetim e metric for this class is given by equation (35); to render this metric ex plicit, one must solve the nonlinear differential equation (31). A subclass of these solutions could correspond to the exterior gravitational fields o f rotating cylindrical systems that emit gravitational radiation. This clas s has a special solution-corresponding to the exact solution (32) of equati on (31)-in common with the Robinson-Trautman gravitational wave spacetimes, namely, the Siklos solution. The properties of rotating gravitational wave s are briefly investigated. In particular, we discuss the energy density of these waves using the gravitational stress-energy tensor.