Axisymmetric Stationary Spacetimes of Constant Scalar Curvature in Four Dimensions

Abstract

In this paper we construct a special class of four dimensional axisymmetric stationary spacetimes whose Ricci scalar is constant but not Einstein. We find that this solution has a ring singularity. At the end, we discuss some numerical results of these spacetimes.

Major revisios: 23 pages, 7 figures, section 4 majorly revised and added subsection about numerical results. An author added. Accepted in Gravitation and Cosmology 2022