  Motivated by the study of entanglement island in the Karch-Randall
braneworld, it has been conjectured and proven in general that entanglement
island is not consistent with long-range (massless) gravity. In this paper, we
provide a careful check of this conclusion in a model of massless gravity that
is constructed using the Karch-Randall braneworld. We show that there is indeed
no entanglement island and hence not a nontrivial Page curve due to the
diffeomorphism invariance if we are studying the correct question which is
though subtle. Moreover, we show that this conclusion is not affected by
deforming the setup with the Dvali--Gabadadze--Porrati (DGP) terms.
Furthermore, we show that the consistency of holography in this model will
provide nontrivial constraints to the DGP parameters. This study provides an
example that causality and holography in anti-de Sitter space can be used to
constrain low energy effective theories. At the end, we clarify several
subtleties in the braneworld gravity which are overlooked in the literature and
we discuss the robustness of the above results against possible coarse-graining
protocols to define a subregion in a gravitational theory.
