Some consequences of a spatially varying cosmological constant in a spherically symmetric distribution of matter

This paper investigates the effects of the spatial variation of the cosmological constant Λ on the spacetime geometry within and outside a massive object. It is seen that the variation of Λ with the radial coordinate introduces non-trivial changes leading to spacetime closing on itself around a massive object. It may also be possible to generate interior solutions that lead to flat rotation curves of galaxies