Islands in Kaluza–Klein black holes

Abstract

AbstractThe newly proposed island formula for entanglement entropy of Hawking radiation is applied to spherically symmetric 4-dimensional eternal Kaluza–Klein (KK) black holes. The “charge” Q of KK black holes quantifies its deviation from Schwarzschild black holes. The impact of Q on the island is studied at late times. The late-time island, whose boundary is located outside but within a Planckian distance of the horizon, is slightly extended by Q. While the no-island entropy grows linearly, the late-time entanglement entropy is given by island configuration with twice the Bekenstein–Hawking entropy. Thus we reproduce the Page curve for the eternal KK black holes. Compared with Schwarzschild results, the Page time is delayed by a factor $$(1+Q/r_h)$$ ( 1 + Q / r h ) and the scrambling time is prolonged by a factor $$(1+Q/r_h)^{1/2}$$ ( 1 + Q / r h ) 1 / 2 . Moreover, the higher-dimensional generalization is presented. Skeptically, there are Planck length scales involved, in which a semi-classical description may break down.