  We carefully investigate the gravitational equations of the brane world, in
which all the matter forces except gravity are confined on the 3-brane in a
5-dimensional spacetime with $Z_2$ symmetry.
  We derive the effective gravitational equations on the brane, which reduce to
the conventional Einstein equations in the low energy limit. {}From our general
argument we conclude that the first Randall & Sundrum-type theory (RS1)
[hep-ph/9905221] predicts that the brane with the negative tension is an
anti-gravity world and hence should be excluded from the physical point of
view. Their second-type theory (RS2) [hep-th/9906064] where the brane has the
positive tension provides the correct signature of gravity. In this latter
case, if the bulk spacetime is exactly anti-de Sitter, generically the matter
on the brane is required to be spatially homogeneous because of the Bianchi
identities. By allowing deviations from anti-de Sitter in the bulk, the
situation will be relaxed and the Bianchi identities give just the relation
between the Weyl tensor and the energy momentum tensor. In the present brane
world scenario, the effective Einstein equations cease to be valid during an
era when the cosmological constant on the brane is not well-defined, such as in
the case of the matter dominated by the potential energy of the scalar field.
