Shell sources of stationary axisymmetric gravitational fields (Q1063886)

A number of solutions for material shell sources of stationary axisymmetric gravitational fields are presented. Explicit solutions are found for shells lying on equipotential hypersurfaces \((g_{tt}=const)\) and generating static ''monopole'' fields in prolate and oblate spheroidal coordinates (Zipoy-Voorhees fields). Numerical solutions are found for shells lying on hypersurfaces of constant \(g_{\phi t}/g_{\phi \phi}\) and generating Kerr- and Tomimatsu-Sato \((\delta =2)\) fields. The shells have minimum areas allowed by the energy conditions of Hawking and Ellis.