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Islands in Kaluza-Klein black holes

High Energy Physics - Theory 2022-02-15 v3 General Relativity and Quantum Cosmology

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" QQ of KK black holes quantifies its deviation from Schwarzschild black holes. The impact of QQ 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 QQ. 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/rh)(1+Q/r_h) and the scrambling time is prolonged by a factor (1+Q/rh)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.

Keywords

Cite

@article{arxiv.2106.07845,
  title  = {Islands in Kaluza-Klein black holes},
  author = {Yizhou Lu and Jiong Lin},
  journal= {arXiv preprint arXiv:2106.07845},
  year   = {2022}
}

Comments

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