Radiation entropy in asymptotically AdS black holes within f(Q) gravity

We employ the island formula to investigate the entanglement entropy of the Hawking radiation in an asymptotically AdS black hole background within the framework of f ( Q ) gravity. Through an analysis based on the Euclidean action, we find that the area term of the generalized entropy must be modified, which in turn leads to a modification of the island formula. Using the modified formula to compute the radiation entropy for an eternal asymptotically AdS black hole reveals that, the result diverges as the cutoff surface is moved outward, indicating the breakdown of the s -wave approximation. A possible reason is that we have neglected the gravitational back-reaction. For a collapsing asymptotically AdS black hole, the radiation entropy is dominated by the area term, with a correction proportional to the logarithm of the event horizon area, which is consistent with the predictions of quantum gravity. Both the radiation entropy and the Page time are ultimately influenced by the choice of the f ( Q ) model, implying that the information regarding the underlying gravitational model is encoded in the final radiation.