Einstein Gravity on a Brane in 5D Non-compact Flat Spacetime

We revisit the 5D gravity model by Dvali, Gabadadze, and Porrati (DGP).Within their framework it was shown that even in 5D non-compact Minkowski space$(x^\mu,z)$, the Newtonian gravity can emerge on a brane at short distances byintroducing a brane-localized 4D Einstein-Hilbert term$\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$ in the action. Based on this idea,we construct simple setups in which graviton standing waves can arise, and weintroduce brane-localized $z$ derivative terms as a correction to$\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$. We show that the gravity potentialof brane matter becomes $-\frac{1}{r}$ at {\it long} distances, because thebrane-localized $z$ derivative terms allow only a smooth graviton wave functionnear the brane. Since the bulk gravity coupling may be arbitrarily small,strongly interacting modes from the 5D graviton do not appear. We note that thebrane metric utilized to construct $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$can be relatively different from the bulk metric by a conformal factor, andshow that the graviton tensor structure that the 4D Einstein gravity predictsare reproduced in DGP type models.Comment: 1+12 pages, no figure, to appear in JHE