Infrared Regularization and Finite Size Dynamics of Entanglement Entropy in Schwarzschild Black Hole
Abstract: In this paper, infrared regularization of semi-infinite entangling regions and island formation for regions of finite size in the eternal Schwarzschild black hole are considered. We analyze whether the complementarity property and pure state condition of entanglement entropy can be preserved in the given approximation. We propose a special regularization that satisfies these two properties. With regard to entangling regions of finite size, we derive two fundamental types of them, which we call "mirror-symmetric" (MS) and "asymmetric" (AS). For MS regions, we discover a discontinuous evolution of the entanglement entropy of Hawking radiation due to finite lifetime of the island. The entanglement entropy of matter for semi-infinite regions in two-sided Schwarzschild black hole does not follow the Page curve. The lifetime of AS regions is bounded from above due to the phenomenon that we call "Cauchy surface breaking". Shortly before this breaking, the island configuration becomes non-symmetric. For both types of finite regions, there is a critical size, below which the island never dominates. For regions smaller than some other critical size, the island does not emerge. Finally, we show that the island prescription does not help to solve the information paradox for certain finite regions.
- S. W. Hawking, Commun. Math. Phys. 43, 199 (1975), [Erratum: Commun.Math.Phys. 46, 206 (1976)].
- S. W. Hawking, Phys. Rev. D 14, 2460 (1976).
- D. N. Page, Phys. Rev. Lett. 71, 3743 (1993), arXiv:hep-th/9306083 .
- D. N. Page, JCAP 09, 028 (2013), arXiv:1301.4995 [hep-th] .
- G. Penington, JHEP 09, 002 (2020), arXiv:1905.08255 [hep-th] .
- P. C. W. Davies and S. A. Fulling, Proc. Roy. Soc. Lond. A 348, 393 (1976).
- P. Chen and D.-h. Yeom, Phys. Rev. D 96, 025016 (2017), arXiv:1704.08613 [hep-th] .
- T. Anegawa and N. Iizuka, JHEP 07, 036 (2020), arXiv:2004.01601 [hep-th] .
- H. Geng and A. Karch, JHEP 09, 121 (2020), arXiv:2006.02438 [hep-th] .
- W. Sybesma, Class. Quant. Grav. 38, 145012 (2021), arXiv:2008.07994 [hep-th] .
- Y. Matsuo, JHEP 07, 051 (2021), arXiv:2011.08814 [hep-th] .
- I. A. Reyes, Phys. Rev. Lett. 127, 051602 (2021), arXiv:2103.01230 [hep-th] .
- W. Kim and M. Nam, Eur. Phys. J. C 81, 869 (2021), arXiv:2103.16163 [hep-th] .
- L. Aalsma and W. Sybesma, JHEP 05, 291 (2021), arXiv:2104.00006 [hep-th] .
- Y. Lu and J. Lin, Eur. Phys. J. C 82, 132 (2022), arXiv:2106.07845 [hep-th] .
- M.-H. Yu and X.-H. Ge, Eur. Phys. J. C 82, 14 (2022), arXiv:2107.03031 [hep-th] .
- D. S. Ageev, JHEP 03, 033 (2022), arXiv:2107.09083 [hep-th] .
- N. H. Cao, Eur. Phys. J. C 82, 381 (2022), arXiv:2108.10144 [hep-th] .
- I. Aref’eva and I. Volovich,  (2021), arXiv:2110.04233 [hep-th] .
- F. Omidi, JHEP 04, 022 (2022), arXiv:2112.05890 [hep-th] .
- K. Suzuki and T. Takayanagi, JHEP 06, 095 (2022), arXiv:2202.08462 [hep-th] .
- S. Azarnia and R. Fareghbal, Phys. Rev. D 106, 026012 (2022), arXiv:2204.08488 [hep-th] .
- A. Anand,  (2022), arXiv:2205.13785 [hep-th] .
- D. S. Ageev and I. Y. Aref’eva, Eur. Phys. J. Plus 137, 1188 (2022), arXiv:2206.04094 [hep-th] .
- K. Goswami and K. Narayan, JHEP 10, 031 (2022), arXiv:2207.10724 [hep-th] .
- S. N. Solodukhin, Living Rev. Rel. 14, 8 (2011), arXiv:1104.3712 [hep-th] .
- T. Nishioka, Rev. Mod. Phys. 90, 035007 (2018), arXiv:1801.10352 [hep-th] .
- J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960 (1983).
- P. Calabrese and J. L. Cardy, J. Stat. Mech. 0406, P06002 (2004), arXiv:hep-th/0405152 .
- P. Calabrese and J. Cardy, J. Phys. A 42, 504005 (2009), arXiv:0905.4013 [cond-mat.stat-mech] .
- T. Hartman and J. Maldacena, JHEP 05, 014 (2013), arXiv:1303.1080 [hep-th] .
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