Axisymmmetric empty space: light propagation, orbits and dark matter

This study presents a axisymmetric solution of the Einstein equations for empty space. The geometry is studied by determining its Petrov classification and Killing vectors. Light propagation, orbital motion and asymptotic and Newtonian limits are also studied. Additionally, cosmological applications of the geometry as an alternative model for the inflationary universe and as a substitute for dark matter and quintessence are also outlined.