  We present a doubly holographic prescription for computing entanglement
entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a
Dirichlet anchoring condition. In braneworld cosmology, a related approach was
used previously in arXiv:2007.06551. There, the prescription naturally computed
a co-moving entanglement entropy, and was argued to resolve the information
paradox for a black hole living in the cosmology. In this paper, we show that
the Dirichlet prescription leads to reasonable results, when applied to a
recently studied wedge holography set up with a gravitating bath. The nature of
the information paradox and its resolution in our Dirichlet problem have a
natural understanding in terms of the strength of gravity on the two branes and
at the anchoring location. By sliding the anchor to the defect, we demonstrate
that the limit where gravity decouples from the anchor is continuous -- in
other words, as far as island physics is considered, weak gravity on the anchor
is identical to no gravity. The weak and (moderately) strong gravity regions on
the brane are separated by a "Dirichlet wall". We find an intricate interplay
between various extremal surfaces, with an island coming to the rescue whenever
there is an information paradox. This is despite the presence of massless
gravitons in the spectrum. The overall physics is consistent with the slogan
that gravity becomes "more holographic", as it gets stronger. Our observations
strengthen the case that the conventional Page curve is indeed of significance,
when discussing the information paradox in flat space. We work in high enough
dimensions so that the graviton is non-trivial, and our results are in line
with the previous discussions on gravitating baths in arXiv:2005.02993 and
arXiv:2007.06551.

High Energy Physics - Theory