Newton law on the generalized singular brane with and without 4d induced gravity

Newton law arising due to the gravity localized on the general singular brane embedded in AdS5 bulk is examined in the absence or presence of the 4d induced Einstein term. For the RS brane, apart from the subleading correction, Newton potential obeys 4d- and 5d-type gravitational law at long- and short-ranges if it were not for the induced Einstein term. The 4d induced Einstein term generates an intermediate range at short distance, in which the 5d Newton potential 1/r2 emerges. For Neumann brane the long-range behavior of Newton potential is exponentially suppressed regardless of the existence of the induced Einstein term. For Dirichlet brane the expression of Newton potential is dependent on the renormalized coupling constant vren. At particular value of vren Newton potential on Dirichlet brane exhibits a similar behavior to that on RS brane. For other values the long-range behavior of Newton potential is exponentially suppressed as that in Neumann brane