Thermal equilibration of brane-worlds

We analyze the thermodynamical properties of brane-worlds, with a focus on the second model of Randall and Sundrum. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk. This leads us to ask the question: can the black hole–brane-world system evolve towards a configuration of thermal equilibrium? To answer this, we generalize the second Randall–Sundrum scenario to allow for non-static bulk regions on each side of the brane-world. 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. Using the background subtraction technique to calculate the Euclidean action, we argue that at late times a sufficiently large black hole will relax to a point of thermal equilibrium with the brane-world environment. These results have interesting implications for early-universe cosmology.