6. Oppenheimer, J. R. and Snyder, H. (1939), ‘On Continued Gravitational Contraction’, Phys. Rev. Lett., 56:455.
7. Wheeler, J. A. with Ford, K. (2000), Geons, Black Holes, and Quantum Foam. A Life in Physics (W. W. Norton & Co., New York).
8. Fuller, R. W. and Wheeler, J. A. (1962), ‘Causality and Multiply Connected Space-Time’, Phys. Rev., 128:919–929.
9. Penrose, R. (1965), ‘Gravitational Collapse and Space-Time Singularities’, Phys. Rev. Lett., 14:57.
10. Hawking, S. W. (1974), ‘Black Hole Explosions?’, Nature, 248: 30–31.
11. Wigner, Eugene P. (1960), ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, Comm. Pure Appl. Math., 13:1, 1–14.
12. Taylor, E. F., Wheeler, J. A. and Bertschinger, E. W. (2000), Exploring Black Holes (Pearson, New York).
13. Page, D. N. (2005), ‘Hawking Radiation and Black Hole Thermodynamics’, New J. Phys., 7:203.
14. Hawking, S. W. (1975), ‘Particle Creation by Black Holes’, Comm. Math. Phys., 43:199–220.
15. Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973), Gravitation (Princeton University Press, Princeton).
16. Hafele, J. C. and Keating, R. E. (1972), Science, 177(4044):168.
17. Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973), Gravitation (Princeton University Press, Princeton).
18. Hamilton, A. J. S. and Lisle, J. P. (2008), ‘The River Model of Black Holes’, Am. J. Phys., 76:519–532.
19. Einstein, A. and Rosen, N. (1935), ‘The Particle Problem in the General Theory of Relativity’, Phys. Rev., 48:73.
20. Taylor, E. F., Wheeler, J. A. and Bertschinger, E. W. (2000), Exploring Black Holes (Pearson, New York).
21. Morris, M., Thorne, K. and Yurtsever, U. (1988), ‘Wormholes, Time Machines and the Weak Energy Condition’, Phys. Rev. Lett., 61(13):1446–1449.
22. Hawking, S., Thorne, K., Novikov, I., Ferris, T., Lightman, A. and Price, R. (2002), The Future of Spacetime (W. W. Norton & Co., New York).
23. Droz, S., Israel, W. and Morsink, S. M. (1996), ‘Black Holes: the Inside Story’, Phys. World, 9(1):34.
24. Chandrasekhar, S. (1987), Truth and Beauty (University of Chicago Press, Chicago).
25. Wheeler, J. A. with Ford, K. (2000), Geons, Black Holes, and Quantum Foam. A Life in Physics (W. W. Norton & Co., New York).
26. Abbott, J. (1879), ‘The New Theory of Heat’, Harper’s New Monthly Magazine, XXXIX.
27. Atkins, P. (2010), The Laws of Thermodynamics: A Very Short Introduction (Oxford University Press, Oxford).
28. Letter to John William Strutt, Baron Rayleigh, dated 6 December 1870.
29. Goodstein, D. L. (2002), States of Matter (Dover Publications, New York).
30. Feynman, R. P. (1997), The Character of Physical Law (Random House, New York).
31. Hawking, S. W. (1974) ‘Black Hole Explosions?’, Nature, 248: 30–31.
32. Bardeen, J. M., Carter, B. and Hawking, S. W. (1973), ‘The Four Laws of Black Hole Mechanics’, Comm. Math. Phys., 31(2):161–170.
33. Hawking, S. W. (1974) ‘Black Hole Explosions?’, Nature, 248: 30–31.
34. From the Proceedings of the third International Symposium on the Foundations of Quantum Mechanics, Tokyo, 1989.
35. Fulling, S. A. (1973), ‘Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time’, Phys. Rev., D., 7(10): 2850. Davies, P. C. W. (1975), ‘Scalar Production in Schwarzschild and Rindler Metrics’, Phys. A., 8(4):609. Unruh, W. G. (1976), ‘Notes on Black-hole Evaporation’, Phys. Rev. D., 14(4):870.
36. Black hole complementarity was first introduced in a paper written in 1993 by Leonard Susskind, Lárus Thorlacius and John Uglum, following earlier work by Gerardus ’t Hooft. Susskind, L., Thorlacius, L., Uglum, J. (1993), ‘The Stretched Horizon and Black Hole Complementarity’, Phys. Rev. D., 48(8):3743. ’t Hooft, G. (1990), ‘The Black Hole Interpretation of String Theory’, Nucl. Phys. B., 335(1):138.
37. Susskind, L. (2008), The Black Hole War (Little Brown, New York).
38. Nielsen, M. A. and Chuang, I. L. (2010), Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge).
39. Kwiat, P. G. and Hardy, L. (2000), ‘The Mystery of the Quantum Cakes’, Am. J. Phys., 68(1):33–36.
40. Page, D. N. (1993), ‘Information in Black Hole Radiation’, Phys. Rev. Lett., 71:3743.
41. Almheiri, A., Marolf, D., Polchinski, J. and Sully, J. (2013), ‘Black Holes: Complementarity or Firewalls?’, J. High Energy Phys., 2013(2).
42. Hayden, P. and Preskill, J. (2007), ‘Black Holes as Mirrors: Quantum Information in Random Subsystems’, J. High Energy Phys., 2007 (9):120.
43. Susskind, L. (1995), ‘The World as a Hologram’, J. Math. Phys., 36:6377–6396.
44. Maldacena, J. (1998), ‘The Large N Limit of Superconformal Field Theories and Supergravity’, Adv. Theor. Math. Phys., 2(4): 231–252.
45. Penington, G. (2020), ‘Entanglement Wedge Reconstruction and the Information Paradox’, J. High Energy. Phys., 2020(9):2.
46. Ryu, S. and Takayanagi, T. (2006), ‘Aspects of Holographic Entanglement Entropy’, J. High Energy Phys., 2006(8):045.
47. Maldacena, J. and Susskind, L. (2013), ‘Cool Horizons for Black Holes’, Fortsch. Phys., 61:781.
48. Einstein, A., Podolsky, B. and Rosen, N. (1935), ‘Can Quantum-mechanical Description of Physical Reality be Considered Complete?’, Phys. Rev., 47(10):777.
49. Almheiri, A., Engelhardt, N., Marolf, D. and Maxfield, H. (2019), ‘The Entropy of Bulk Quantum Fields and the Entanglement Wedge of an Evaporating Black Hole’, J. High Energy Phys., 2019(12):63. Penington, G., ‘Entanglement Wedge Reconstruction and the Information Paradox’, J. High Energy Phys., 2020(9):2.
50. From the Proceedings of the third International Symposium on the Foundations of Quantum Mechanics, Tokyo, 1989.
51. ibid.
52. Almheiri, A., Dong, X. and Harlow, D. (2015), ‘Bulk Locality and Quantum Error Correction in AdS/CFT’, JHEP, 04:163.
53. Pastawski, F., Yoshida, B., Harlow, D. and Preskill, J. (2015), ‘Holographic Quantum Error-correcting Codes: Toy Models for the Bulk/Boundary Correspondence’, JHEP, 06:149.
Index
The page numbers in this index relate to the printed version of this book; they do not match the pages of your ebook. You can use your ebook reader’s search tool to find a specific word or passage.
Abbott, Edwin, 42
Abbott, Jacob, 166
absolute zero temperature, 17, 172–6, 189–90
accelerating observer, 64–72, 98–105, 113–14
quantum effects, 197–8
Adams, Douglas, 56
AdS/CFT correspondence, 236–40
age as length of worldline, 33, 62–6
Agnew, Jonathan, 27–8
Akhtar, Shoaib, 25–8
Almheiri, Ahmed, 228, 258
‘AMPS’ paper, 228–31, 245
Andromeda galaxy, 66, 210
anti-de Sitter spacetime (AdS), 236–8
anti-gravity universe, 140
arrangements, number of, 171–8, 221–2
arrow of time, thermodynamic, 177