  We study the brane world motion in non-static bulk by generalizing the second
Randall-Sundrum scenario Explicitly, we take the bulk to be a Vaidya-AdS
metric, which describes the gravitational collapse of a spherically symmetric
null dust fluid in Anti-de Sitter spacetime. We point out that during an
inflationary phase on the brane, black holes will tend to be thermally
nucleated in the bulk We analyze the thermodynamical properties of this
brane-world.We point out that during an inflationary phase on the brane, black
holes will tend to be thermally nucleated in the bulk. Thermal equilibrium of
the system is discussed. We calculate the late time behavior of this system,
including 1-loop effects. We argue that at late times a sufficiently large
black hole will relax to a point of thermal equilibrium with the brane-world
environment. This result has interesting implications for early-universe
cosmology.
