Islands in Kaluza-Klein black holes

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.

20 pages, 3 figures; Corrected some mistakes including the missing of the modification of the horizon area and the discussion of the case if island is inside the horizon

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Cited by in corpus (17)

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• BCFT in a Black Hole Background: An Analytical Holographic Model
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• Cosmological and black hole islands in multi-event horizon spacetimes
• Planar Black Holes in Holographic Axion Gravity: Islands, Page Times, and Scrambling Times
• Page Curve of Effective Hawking Radiation
• The Markov gap in the presence of islands
• Unitary Constraints on Semiclassical Schwarzschild Black Holes in the Presence of Island
• Entanglement entropy and Page curve of black holes with island in massive gravity
• Defect extremal surfaces for entanglement negativity
• Entanglement between two evaporating black holes
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Infrared Regularization and Finite Size Dynamics of Entanglement Entropy in Schwarzschild Black Hole
• A comment on a fine-grained description of evaporating black holes with baby universes
• Encoded information of mixed correlations: the views from one dimension higher