Journal of the Korean Physical Society

Korean Physical Society (한국물리학회)
권호 표지
DOI QR코드

DOI QR Code

How Can We Erase States Inside a Black Hole?

  • Hwang, Junha (School of Undergraduate Studies, College of Transdisciplinary Studies, Daegu Gyeongbuk Institute of Science and Technology (DGIST)) ;
  • Park, Hyosub (School of Undergraduate Studies, College of Transdisciplinary Studies, Daegu Gyeongbuk Institute of Science and Technology (DGIST)) ;
  • Yeom, Dong-han (Asia Pacific Center for Theoretical Physics, Department of Physics, POSTECH) ;
  • Zoe, Heeseung (School of Undergraduate Studies, College of Transdisciplinary Studies, Daegu Gyeongbuk Institute of Science and Technology (DGIST))
  • Received : 2018.03.16
  • Accepted : 2018.07.02
  • Published : 2018.11.30
⟨ Previous Next ⟩

Abstract

We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero energy system by maintaining unitarity. In this paper, based on some toy model calculations, we show that such a unitary tracing-out process is only possible before the Page time while it is impossible after the Page time. Hence, after the Page time, if we assume that the process is unitary and the Hawking pair forms a separable state, the internal number of states will monotonically increase, which is supported by the Almheiri-Marolf-Polchinski-Sully (AMPS) argument. In addition, the Hawking particles cannot generate randomness of the entire system; hence, the entanglement entropy cannot reach its maximum. Based on these results, we modify the correct form of the Page curve for the remnant picture. The most important conclusion is this: if we assume unitarity, semi-classical quantum field theory, and general relativity, then the black hole should violate the Bekenstein-Hawking entropy bound around the Page time at the latest; hence, the infinite production arguments for remnants might be applied for semi-classical black holes, which seems very problematic.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea

References

  1. S. W. Hawking, Phys. Rev. D 14, 2460 (1976). https://doi.org/10.1103/PhysRevD.14.2460
  2. D. N. Page, Phys. Rev. Lett. 71, 1291 (1993) [arXiv:gr-qc/9305007] https://doi.org/10.1103/PhysRevLett.71.1291
  3. D. N. Page, Phys. Rev. Lett. 71, 3743 (1993) [arXiv:hep-th/9306083] https://doi.org/10.1103/PhysRevLett.71.3743
  4. D. N. Page, JCAP 1309, 028 (2013) [arXiv:1301.4995 [hep-th]].
  5. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975) Erratum: [Commun. Math. Phys. 46, 206 (1976)]. https://doi.org/10.1007/BF01608497
  6. J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).
  7. L. Susskind, L. Thorlacius and J. Uglum, Phys. Rev. D 48, 3743 (1993) [arXiv:hep-th/9306069]. https://doi.org/10.1103/PhysRevD.48.3743
  8. D. Yeom and H. Zoe, Phys. Rev. D 78, 104008 (2008) [arXiv:0802.1625 [gr-qc]] https://doi.org/10.1103/PhysRevD.78.104008
  9. S. E. Hong, D. Hwang, E. D. Stewart and D. Yeom, Class. Quant. Grav. 27, 045014 (2010) [arXiv:0808.1709 [gr-qc]] https://doi.org/10.1088/0264-9381/27/4/045014
  10. D. Yeom, Int. J. Mod. Phys. Conf. Ser. 1, 311 (2011) [arXiv:0901.1929 [gr-qc]] https://doi.org/10.1142/S2010194511000456
  11. D. Yeom and H. Zoe, Int. J. Mod. Phys. A 26, 3287 (2011) [arXiv:0907.0677 [hep-th]] https://doi.org/10.1142/S0217751X11053924
  12. P. Chen, Y. C. Ong and D. Yeom, JHEP 1412, 021 (2014) [arXiv:1408.3763 [hep-th]].
  13. A. Almheiri, D. Marolf, J. Polchinski and J. Sully, JHEP 1302, 062 (2013) [arXiv:1207.3123 [hep-th]]
  14. A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, JHEP 1309, 018 (2013) [arXiv:1304.6483 [hep-th]].
  15. P. Chen, Y. C. Ong and D. Yeom, Phys. Rept. 603, 1 (2015) [arXiv:1412.8366 [gr-qc]]. https://doi.org/10.1016/j.physrep.2015.10.007
  16. J. Hwang, D. S. Lee, D. Nho, J. Oh, H. Park, D. Yeom and H. Zoe, Class. Quant. Grav. 34, 145004 (2017) [arXiv:1608.03391 [hep-th]]. https://doi.org/10.1088/1361-6382/aa76a5
  17. P. C. W. Davies, S. A. Fulling and W. G. Unruh, Phys. Rev. D 13, 2720 (1976). https://doi.org/10.1103/PhysRevD.13.2720
  18. P. Chen and D. Yeom, Phys. Rev. D 96, 025016 (2017) [arXiv:1704.08613 [hep-th]] https://doi.org/10.1103/PhysRevD.96.025016
  19. M. R. R. Good and Y. C. Ong, JHEP 1507, 145 (2015) [arXiv:1506.08072 [gr-qc]].
  20. M. Hotta and A. Sugita, PTEP 2015, 123B04 (2015) [arXiv:1505.05870 [gr-qc]]
  21. M. Hotta, Y. Nambu and K. Yamaguchi, arXiv:1706.07520 [gr-qc]. https://doi.org/10.1103/PhysRevLett.120.181301
  22. Y. C. Ong and D. Yeom, arXiv:1602.06600 [hep-th].
  23. W. G. Unruh and R. M. Wald, Phys. Rev. D 52, 2176 (1995) [arXiv:hep-th/9503024]. https://doi.org/10.1103/PhysRevD.52.2176
  24. J. M. Maldacena, JHEP 0304, 021 (2003) [arXiv:hep-th/0106112]
  25. S. W. Hawking, Phys. Rev. D 72, 084013 (2005) [arXiv:hep-th/0507171] https://doi.org/10.1103/PhysRevD.72.084013
  26. S. W. Hawking, arXiv:1401.5761 [hep-th].
  27. M. Sasaki and D. Yeom, JHEP 1412, 155 (2014) [arXiv:1404.1565 [hep-th]]
  28. B. H. Lee, W. Lee and D. Yeom, Phys. Rev. D 92, 024027 (2015) [arXiv:1502.07471 [hep-th]] https://doi.org/10.1103/PhysRevD.92.024027
  29. P. Chen, G. Domenech, M. Sasaki and D. Yeom, JCAP 1604, 013 (2016) [arXiv:1512.00565 [hep-th]]
  30. P. Chen, Y. C. Hu and D. Yeom, Phys. Rev. D 94, 024044 (2016) [arXiv:1512.03914 [hep-th]]. https://doi.org/10.1103/PhysRevD.94.024044
  31. G. T. Horowitz and J. M. Maldacena, JHEP 0402, 008 (2004) [arXiv:hep-th/0310281].
  32. D. N. Page, JCAP 1406, 051 (2014) [arXiv:1306.0562 [hep-th]].
  33. A. Alonso-Serrano and M. Visser, Phys. Lett. B 776, 10 (2018) [arXiv:1512.01890 [gr-qc]]. https://doi.org/10.1016/j.physletb.2017.11.020
  34. S. Lloyd and H. Pagels, Annals Phys. 188, 186 (1988). https://doi.org/10.1016/0003-4916(88)90094-2
  35. S. B. Giddings, Phys. Rev. D 51, 6860 (1995) [arXiv:hep-th/9412159]. https://doi.org/10.1103/PhysRevD.51.6860
  36. D. Hwang, B-H. Lee and D. Yeom, JCAP 1301, 005 (2013) [arXiv:1210.6733 [gr-qc]]
  37. W. Kim, B-H. Lee and D. Yeom, JHEP 1305, 060 (2013) [arXiv:1301.5138 [gr-qc]]
  38. B-H. Lee and D. Yeom, Nucl. Phys. Proc. Suppl. 246-247, 178 (2014) [arXiv:1302.6006 [gr-qc]] https://doi.org/10.1016/j.nuclphysbps.2013.10.082
  39. P. Chen, Y. C. Ong, D. N. Page, M. Sasaki and D. Yeom, Phys. Rev. Lett. 116, 161304 (2016) [arXiv:1511.05695 [hep-th]]. https://doi.org/10.1103/PhysRevLett.116.161304

Cited by

  1. Finite energy but infinite entropy production from moving mirrors vol.99, pp.2, 2018, https://doi.org/10.1103/physrevd.99.025009
  2. Causal structures and dynamics of black-hole-like solutions in string theory vol.79, pp.11, 2019, https://doi.org/10.1140/epjc/s10052-019-7435-7
  3. Demonstration of the Hayden-Preskill Protocol via Mutual Information vol.75, pp.12, 2018, https://doi.org/10.3938/jkps.75.941
  4. Finite thermal particle creation of Casimir light vol.35, pp.3, 2020, https://doi.org/10.1142/s0217732320400064
  5. Nonextensive black hole entropy and quantum gravity effects at the last stages of evaporation vol.103, pp.2, 2021, https://doi.org/10.1103/physrevd.103.026021
  6. Modified Schwarzschild metric from a unitary accelerating mirror analog vol.23, pp.4, 2021, https://doi.org/10.1088/1367-2630/abe506
  7. Almost certain loss from black holes: critical comments on the black hole final-state proposal vol.79, pp.3, 2018, https://doi.org/10.1007/s40042-021-00203-1
  8. Ellis wormholes in anti-de Sitter space vol.81, pp.9, 2018, https://doi.org/10.1140/epjc/s10052-021-09645-0