Islands in Kaluza-Klein black holes

TL;DR

This paper applies the island formula to Kaluza-Klein black holes, revealing how charge affects entanglement entropy and reproducing the Page curve, with implications for black hole information paradox studies.

Contribution

It extends the island formula application to charged KK black holes, analyzing the impact of charge on entanglement entropy and the Page curve in higher-dimensional contexts.

Findings

Late-time island boundary extends with charge Q.

Page time is delayed by factor (1+Q/r_h).

Scrambling time is prolonged by factor (1+Q/r_h)^{1/2}.

Abstract

The newly proposed island formula for entanglement entropy of Hawking radiation is applied to spherically symmetric 4-dimensional eternal Kaluza-Klein (KK) black hole. 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 $(1+Q/r_h)$ and the scrambling time is prolonged by a factor $(1+Q/r_h)^{1/2}$. Moreover, the higher-dimensional generalization is presented. Skeptically, there are Planck length scales involved, in which a semi-classical description may break down.