Geodesics on metrics of Eguchi–Hanson type

Abstract

AbstractGeodesic equations are solved when at least two of $$\theta $$ θ , $$\phi $$ ϕ and $$\psi $$ ψ are constant, or r is constant, on scalar flat metrics of Eguchi–Hanson type. They can also be solved also on Eguchi–Hanson metrics which are Ricci flat if only $$\phi $$ ϕ is constant. However, the explicit solution of the geodesic equations is not available yet if only $$\psi $$ ψ is constant.