The covariant entropy bound in gravitational collapse

Abstract

We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, $L$, of the old black hole then terminates at the singularity. We show that the entropy crossing $L$ does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process.