  We generalize the results of Randall and Sundrum to a wider class of
four-dimensional space-times including the four-dimensional Schwarzschild
background and de Sitter universe. We solve the equation for graviton
propagation in a general four dimensional background and find an explicit
solution for a zero mass bound state of the graviton. We find that this zero
mass bound state is normalizable only if the cosmological constant is strictly
zero, thereby providing a dynamical reason for the vanishing of cosmological
constant within the context of this model. We also show that the results of
Randall and Sundrum can be generalized without any modification to the
Schwarzschild background.
