On cosmological constant of Generalized Robertson-Walker space-times

We study Einstein's equation in $(m+n)D$ and $(1+n)D$ warped spaces $(\bar{M},\bar{g})$ and classify all such spaces satisfying Einstein equations $\bar{G}=-\bar{\Lambda}\bar{g}$. We show that the warping function not only can determine the cosmological constant $\bar{\Lambda}$ but also it can determine the cosmological constant ${\Lambda}$ appearing in the induced Einstein equations ${G}=-{\Lambda}{h}$ on $(M_2, h)$. Moreover, we discuss on the origin of the $4D$ cosmological constant as an emergent effect of higher dimensional warped spaces.