Information transfer with a gravitating bath

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended gravitational systems. To gain insight into question, we explore story modified within context Karch-Randall braneworlds when allow bath couple dynamical gravity. We find that because inability separate degrees freedom by spatial location defining radiation region, entropy emitted time-independent constant, consistent with recent work on hole asymptotically flat space. If instead consider between two sectors specific division Hilbert space, then non-trivial time-dependence, Page time monotonically decreasing function brane angle---provided both branes are below particular angle. However, properties depend discontinuously angle, which first example such discontinuous behavior