Conformally flat stationary axisymmetric spacetimes

It is shown that within conformally flat stationary axisymmetric spacetimes, in addition to the locally static family, there exists a new class of metrics, which is always stationary and axisymmetric. All these spacetimes, the static and the stationary ones, are endowed with an arbitrary function depending on the two non-Killingian coordinates. The explicit form of this function can be determined once the coupled matter, i.e., the energy-momentum tensor, is given. The locally static branch allows for horizons, and hence for the existence of black hole solutions, while the intrinsic stationary axisymmetric family does not permit black holes. Since both classes of metrics allow for surfaces possessing an extrinsic curvature proportional to their intrinsic metrics, there is room for the possibility of constructing two-branes in these spacetimes.