  Two flat Randall - Sundrum three-branes are analyzed, at fixed mutual
distance, in the case where each brane contains an ideal isotropic fluid. Both
fluids are to begin with assumed to obey the equation of state p=(\gamma
-1)\rho, where \gamma is a constant. Thereafter, we impose the condition that
there is zero energy flux from the branes into the bulk, and assume that the
tension on either brane is zero. It then follows that constant values of the
fluid energies at the branes are obtained only if the value of \gamma is equal
to zero (i.e., a `vacuum' fluid). The fluids on the branes are related: if one
brane is a dS_4 brane (the effective four-dimensional constant being positive),
then the other brane is dS_4 also, and if the fluid energy density on one brane
is positive, the energy density on the other brane is larger in magnitude but
negative. This is a non-acceptable result, which sheds some light on how far it
is possible to give a physical interpretation of the two-brane scenario. Also,
we discuss the graviton localization problem in the two-brane setting,
generalizing prior works.
