Radiation Entropy in asymptotically AdS Black Holes within f(Q) Gravity

Abstract

We employ the island rule to investigate the radiation entropy of asymptotically AdS black holes in 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 rule itself. Using the corrected rule to compute the radiation entropy for the 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. For a collapsing asymptotically AdS black hole, the radiation entropy is dominated by the area term, with a logarithmic correction proportional to the area, which is consistent with the predictions of quantum gravity theories. Furthermore, both the radiation entropy and the Page time are ultimately influenced by the choice of the f(Q) model, implying that information regarding the underlying gravitational model is encoded in the final radiation entropy.