Computational complexity and black hole horizons
Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely d...
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| Veröffentlicht in: | Fortschritte der Physik Jg. 64; H. 1; S. 24 - 43 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Weinheim
Blackwell Publishing Ltd
01.01.2016
Wiley Subscription Services, Inc |
| Schlagworte: | |
| ISSN: | 0015-8208, 1521-3978 |
| Online-Zugang: | Volltext |
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| Abstract | Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely difficult and probably impossible for black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity.
Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity. |
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| AbstractList | Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely difficult and probably impossible for black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity. Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find that while creating firewalls is possible, it is extremely difficult and probably impossible for black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity. Computational complexity is essential to understanding the properties of black hole horizons. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. In general we find black holes that form in sudden collapse, and then evaporate. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity. |
| Author | Susskind, Leonard |
| Author_xml | – sequence: 1 givenname: Leonard surname: Susskind fullname: Susskind, Leonard email: susskind@stanford.edu organization: Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, CA, 94305-4060, Stanford, USA |
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| Copyright | 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim Copyright © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. All rights reserved |
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| References_xml | – reference: A. Sen, "Black hole solutions in heterotic string theory on a torus," Nucl. Phys. B 440, 421 (1995) [hep-th/9411187]. – reference: Y. Sekino and L. Susskind, "Fast Scramblers," JHEP 0810, 065 (2008) [arXiv:0808.2096 [hep-th]]. – reference: R. Bousso, "Vacuum Structure and the Arrow of Time," Phys. Rev. D 86, 123509 (2012) [arXiv:1112.3341 [hep-th]]. – reference: I. R. Klebanov and L. Susskind, "Continuum Strings From Discrete Field Theories," Nucl. Phys. B 309, 175 (1988). – reference: A. Hamilton, D. N. Kabat, G. Lifschytz, and D. A. Lowe, "Local bulk operators in AdS/CFT: A Boundary view of horizons and locality," Phys. Rev. D 73, 086003 (2006) [hep-th/0506118]. – reference: J. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975). – reference: L. Dyson, M. Kleban, and L. Susskind, "Disturbing implications of a cosmological constant," JHEP 0210, 011 (2002) [hep-th/0208013]. – reference: N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, "Towards the Fast Scrambling Conjecture," JHEP 1304, 022 (2013) [arXiv:1111.6580 [hep-th]]. – reference: E. Halyo, B. Kol, A. Rajaraman, and L. Susskind, "Counting Schwarzschild and charged black holes," Phys. Lett. B 401, 15 (1997) [hep-th/9609075]. – reference: T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995) [gr-qc/9504004]. – reference: L. Susskind, L. Thorlacius, and J. Uglum, "The Stretched horizon and black hole complementarity," Phys. Rev. D 48, 3743 (1993) [hep-th/9306069]. – reference: J. G. Russo and L. Susskind, "Asymptotic level density in heterotic string theory and rotating black holes," Nucl. Phys. B 437, 611 (1995) [hep-th/9405117]. – reference: G. T. Horowitz and J. Polchinski, "A Correspondence principle for black holes and strings," Phys. Rev. D 55, 6189 (1997) [hep-th/9612146]. – reference: M. Van Raamsdonk, "Building up spacetime with quantum entanglement," Gen. Rel. Grav. 42, 2323 (2010) [Int. J. Mod. Phys. D 19, 2429 (2010)] [arXiv:1005.3035 [hep-th]]. – reference: D. Harlow, S. H. Shenker, D. Stanford, and L. Susskind, "Tree-like structure of eternal inflation: A solvable model," Phys. Rev. D 85, 063516 (2012) [arXiv:1110.0496 [hep-th]]. – reference: W. Israel, "Thermo field dynamics of black holes," Phys. Lett. A 57, 107 (1976). – reference: E. P. Verlinde, "On the Origin of Gravity and the Laws of Newton," JHEP 1104, 029 (2011) [arXiv:1001.0785 [hep-th]]. – reference: A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, "Black Holes: Complementarity or Firewalls?," JHEP 1302, 062 (2013) [arXiv:1207.3123 [hep-th]]. – reference: P. Hayden and J. Preskill, "Black holes as mirrors: Quantum information in random subsystems," JHEP 0709, 120 (2007) [arXiv:0708.4025 [hep-th]]. – reference: J. M. Maldacena, "Eternal black holes in anti-de Sitter," JHEP 0304, 021 (2003) [hep-th/0106112]. – reference: T. Hartman and J. Maldacena, "Time Evolution of Entanglement Entropy from Black Hole Interiors," JHEP 1305, 014 (2013) [arXiv:1303.1080 [hep-th]]. – reference: A. W. Peet, "Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states," Nucl. Phys. B 456, 732 (1995) [hep-th/9506200]. – reference: B. Czech, J. L. Karczmarek, F. Nogueira, and M. Van Raamsdonk, "Rindler Quantum Gravity," Class. Quant. Grav. 29, 235025 (2012) [arXiv:1206.1323 [hep-th]]. – volume: 0709 start-page: 120 year: 2007 article-title: Black holes as mirrors: Quantum information in random subsystems publication-title: JHEP – volume: 29 start-page: 235025 year: 2012 article-title: Rindler Quantum Gravity publication-title: Class. Quant. Grav. – volume: 48 start-page: 3743 year: 1993 article-title: The Stretched horizon and black hole complementarity publication-title: Phys. Rev. D – volume: 0810 start-page: 065 year: 2008 article-title: Fast Scramblers publication-title: JHEP – article-title: Quantum Computation vs. Firewalls – volume: 437 start-page: 611 year: 1995 article-title: Asymptotic level density in heterotic string theory and rotating black holes publication-title: Nucl. Phys. B – volume: 309 start-page: 175 year: 1988 article-title: Continuum Strings From Discrete Field Theories publication-title: Nucl. Phys. B – volume: 73 start-page: 086003 year: 2006 article-title: Local bulk operators in AdS/CFT: A Boundary view of horizons and locality publication-title: Phys. Rev. D – volume: 401 start-page: 15 year: 1997 article-title: Counting Schwarzschild and charged black holes publication-title: Phys. Lett. B – volume: 0210 start-page: 011 year: 2002 article-title: Disturbing implications of a cosmological constant publication-title: JHEP – volume: 75 start-page: 1260 year: 1995 publication-title: Phys. Rev. Lett. – volume: 1302 start-page: 062 year: 2013 article-title: Black Holes: Complementarity or Firewalls? publication-title: JHEP – volume: 55 start-page: 6189 year: 1997 article-title: A Correspondence principle for black holes and strings publication-title: Phys. Rev. D – volume: 86 start-page: 123509 year: 2012 article-title: Vacuum Structure and the Arrow of Time publication-title: Phys. Rev. D – volume: 42 start-page: 2323 year: 2010 article-title: Building up spacetime with quantum entanglement publication-title: Gen. Rel. Grav. – volume: 1104 start-page: 029 year: 2011 article-title: On the Origin of Gravity and the Laws of Newton publication-title: JHEP – article-title: Evaporating Firewalls – volume: 0304 start-page: 021 year: 2003 article-title: Eternal black holes in anti‐de Sitter publication-title: JHEP – volume: 57 start-page: 107 year: 1976 article-title: Thermo field dynamics of black holes publication-title: Phys. Lett. A – article-title: Black holes and the butterfly effect – volume: 1304 start-page: 022 year: 2013 article-title: Towards the Fast Scrambling Conjecture publication-title: JHEP – volume: 85 start-page: 063516 year: 2012 article-title: Tree‐like structure of eternal inflation: A solvable model publication-title: Phys. Rev. D – volume: 456 start-page: 732 year: 1995 article-title: Entropy and supersymmetry of D‐dimensional extremal electric black holes versus string states publication-title: Nucl. Phys. B – volume: 1305 start-page: 014 year: 2013 article-title: Time Evolution of Entanglement Entropy from Black Hole Interiors publication-title: JHEP – volume: 11 start-page: 395 year: 1975 publication-title: Phys. Rev. D – volume: 440 start-page: 421 year: 1995 article-title: Black hole solutions in heterotic string theory on a torus publication-title: Nucl. Phys. 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