Island in Quark Cloud Model

We compute the entanglement entropy of Hawking radiation in a bath attached to a deformed eternal AdS black hole dual to field theories where each theory is backreacted by the presence of a uniform static distribution of heavy fundamental quarks. The entanglement entropy of the Hawking radiation increases linearly with time until an island emerges after the Page time, at that point the entanglement entropy saturates to a constant value twice the Bekenstein-Hawking entropy of the deformed black hole resulting in the Page curve. Furthermore, we study the effects of the backreaction on the Page curve and observe that introducing deformation delays the appearance of island and shifts the Page curve to a later time.Comment: 19 pages, 5 figure