Brane worlds: the gravity of escaping matter

Within the framework of a five-dimensional model with one 3-brane and an infinite extra dimension, we discuss a process in which matter escapes from the brane and propagates into the bulk to arbitrarily large distances. An example is a decay of a particle of mass 2m residing on the brane into two particles of mass m that leave the brane and accelerate away. We calculate, in the linearized theory, the metric induced by these particles on the brane. This metric does not obey the four-dimensional Einstein equations and corresponds to a spherical gravity wave propagating along the four-dimensional future lightcone. The four-dimensional spacetime left behind the spherical wave is flat, so the gravitational field induced in the brane world by matter escaping from the brane disappears in a causal way.