Non-spherical sources of Schwarzschild space-time

Abstract While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, inverse not true. Thus, in this manuscript, we find exact axially and static (interior) solutions to Einstein equations, which match smoothly on boundary surface (exterior) even though endowed with symmetry. The are obtained by using general approach outlined Hernández-Pastora et al. (Class Quantum Gravity 33:235005, 2016), satisfy usual requirements imposed physically admissible interior solution. A discussion about physical geometric properties of presented. relativistic multipole moments ( RMM ) explicitly calculated terms variables, allowing prove sources can space-time. complexity evaluated through factors. It shown there one independent factor, as case.