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Making sense of the bizarre behavior of horizons in the McVittie spacetime

Valerio Faraoni*

Andres F. Zambrano Moreno

Roshina Nandra

  • Physics Department and STAR Research Cluster, Bishop’s University, 2600 College Street, Sherbrooke, Québec, Canada J1M 1Z7

  • Physics Department, Bishop’s University, 2600 College Street, Sherbrooke, Québec, Canada J1M 1Z7

  • Astrophysics Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom and Kavli Institute for Cosmology, c/o Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom

  • *vfaraoni@ubishops.ca
  • azambrano07@ubishops.ca
  • rn288@mrao.cam.ac.uk

Phys. Rev. D 85, 083526 – Published 26 April, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.083526

Abstract

The bizarre behavior of the apparent (black hole and cosmological) horizons of the McVittie spacetime is discussed using, as an analogy, the Schwarzschild-de Sitter-Kottler spacetime (which is a special case of McVittie anyway). For a dust-dominated “background” universe, a black hole cannot exist at early times because its (apparent) horizon would be larger than the cosmological (apparent) horizon. A phantom-dominated background universe causes this situation, and the horizon behavior, to be time-reversed.

Article Text

References (47)

  1. G. C. McVittie, Mon. Not. R. Astron. Soc. 93, 325 (1933).
  2. R. Sussman, Gen. Relativ. Gravit. 17, 251 (1985); A. Krasinski, Inhomogeneous Cosmological Models (Cambridge University Press, Cambridge, England, 1997).
  3. B. C. Nolan, Phys. Rev. D 58, 064006 (1998); Classical Quantum Gravity 16, 1227 (1999); 16, 3183 (1999).
  4. N. Kaloper, M. Kleban, and D. Martin, Phys. Rev. D 81, 104044 (2010).
  5. R. Nandra, A. N. Lasenby, and M. P. Hobson, arXiv:1104.4447 [Mon. Not. R. Astron. Soc. (to be published)]; arXiv:1104.4458 [Mon. Not. R. Astron. Soc. (to be published).
  6. K. Lake and M. Abdelqader, Phys. Rev. D 84, 044045 (2011).
  7. V. Faraoni and A. Jacques, Phys. Rev. D 76, 063510 (2007).
  8. C. Gao, X. Chen, V. Faraoni, and Y.-G. Shen, Phys. Rev. D 78, 024008 (2008).
  9. V. Faraoni, C. Gao, X. Chen, and Y.-G. Shen, Phys. Lett. B 671, 7 (2009).
  10. V. Husain, E. A. Martinez, and D. Nuñez, Phys. Rev. D 50, 3783 (1994).
  11. O. A. Fonarev, Classical Quantum Gravity 12, 1739 (1995); H. Maeda, arXiv:0704.2731.
  12. J. Sultana and C. C. Dyer, Gen. Relativ. Gravit. 37, 1347 (2005).
  13. M. L. McClure and C. C. Dyer, Classical Quantum Gravity 23, 1971 (2006); Gen. Relativ. Gravit. 38, 1347 (2006).
  14. D. A. Szafron and J. Wainwright, J. Math. Phys. (N.Y.) 18, 1668 (1977).
  15. D. A. Szafron, J. Math. Phys. (N.Y.) 18, 1673 (1977).
  16. J. D. Barrow and J. Stein-Schabes, Phys. Lett. 103A, 315 (1984); D. J. Shaw and J. D. Barrow, Phys. Rev. D 73, 123505 (2006).
  17. A. Krasinski and C. Hellaby, Phys. Rev. D 69, 043502 (2004); P. Jacewicz and A. Krasinski, Gen. Relativ. Gravit. 44, 81 (2011); C. Gao, X. Chen, Y.-G. Shen, and V. Faraoni, Phys. Rev. D 84, 104047 (2011).
  18. I. Booth, L. Brits, J. A. Gonzalez, and C. Van Den Broeck, Classical Quantum Gravity 23, 413 (2006).
  19. S. N. G. Thakurta, Indian J. Phys. B 55, 304 (1981); D. Kastor and J. H. Traschen, Phys. Rev. D 47, 5370 (1993); M. L. McClure, K. Anderson, and K. Bardahl, arXiv:0709.3288; Phys. Rev. D 77, 104008 (2008); M. Nozawa and H. Maeda, Classical Quantum Gravity 25, 055009 (2008); K. Maeda, N. Ohta, and K. Uzawa, J. High Energy Phys. 06 (2009) 051; C.-Y. Sun, arXiv:0906.3783; Commun. Theor. Phys. 55, 597 (2011); J. T. Firouzjaee and R. Mansouri, Gen. Relativ. Gravit. 42, 2431 (2010); B. J. Carr, T. Harada, and H. Maeda, Classical Quantum Gravity 27, 183101 (2010); H. Culetu, arXiv:1201.3769.
  20. N. Sakai and J. D. Barrow, Classical Quantum Gravity 18, 4717 (2001); T. Clifton, D. F. Mota, and J. D. Barrow, Mon. Not. R. Astron. Soc. 358, 601 (2005).
  21. T. Clifton, Classical Quantum Gravity 23, 7445 (2006).
  22. V. Faraoni, Classical Quantum Gravity 26, 195013 (2009).
  23. A. Einstein and E. G. Straus, Rev. Mod. Phys. 17, 120 (1945); 18, 148 (1946).
  24. J. Pachner, Phys. Rev. 132, 1837 (1963); 137, B1379 (1965); W. M. Irvine, Ann. Phys. (N.Y.) 32, 322 (1965); R. H. Dicke and P. J. E. Peebles, Phys. Rev. Lett. 12, 435 (1964); C. Callan, R. H. Dicke, and P. J. E. Peebles, Am. J. Phys. 33, 105 (1965); P. D’Eath, Phys. Rev. D 11, 1387 (1975); R. P. A. Newman and G. C. McVittie, Gen. Relativ. Gravit. 14, 591 (1982); R. Gautreau, Phys. Rev. D 29, 198 (1984); P. A. Hogan, Astrophys. J. 360, 315 (1990); J. L. Anderson, Phys. Rev. Lett. 75, 3602 (1995); W. B. Bonnor, Mon. Not. R. Astron. Soc. 282, 1467 (1996); A. Feinstein, J. Ibanez, and R. Lazkoz, Astrophys. J. 495, 131 (1998); K. R. Nayak, M. A. H. MacCallum, and C. V. Vishveshwara, Phys. Rev. D 63, 024020 (2000); V. Guruprasad, arXiv:gr-qc/0005090; arXiv:gr-qc/0005014; G. A. Baker, Jr., arXiv:astro-ph/0003152; A. Dominguez and J. Gaite, Europhys. Lett. 55, 458 (2001); T. M. Davis and C. H. Lineweaver, AIP Conf. Proc. 555, 348 (2001); G. F. R. Ellis, Int. J. Mod. Phys. A 17, 2667 (2002); C. Stornaiolo, Gen. Relativ. Gravit. 34, 2089 (2002); T. M. Davis, C. H. Lineweaver, and J. K. Webb, Am. J. Phys. 71, 358 (2003); L. Lindegren and D. Dravins, Astron. Astrophys. 401, 1185 (2003); C. J. Gao, Classical Quantum Gravity 21, 4805 (2004); T. M. Davis and C. H. Lineweaver, Publ. Astron. Soc. Pac. 21, 97 (2004); T. M. Davis, Ph.D. thesis, University of New South Wales, 2003, arXiv:astro-ph/0402278; D. P. Sheehan and V. G. Kriss, arXiv:astro-ph/0411299; W. J. Clavering, Am. J. Phys. 74, 745 (2006); Z.-H. Li and A. Wang, Mod. Phys. Lett. A 22, 1663 (2007); O. Gron and O. Elgaroy, arXiv:astro-ph/0603162 [Am. J. Phys. (to be published)]; L. A. Barnes, M. J. Francis, J. B. James, and G. F. Lewis, Mon. Not. R. Astron. Soc. 373, 382 (2006); R. Lieu and D. A. Gregory, arXiv:astro-ph/0605611; P. K. F. Kuhfittig, Int. J. Pure Appl. Math. 49, 577 (2008); G. S. Adkins, J. McDonnell, and R. N. Fell, Phys. Rev. D 75, 064011 (2007); D. L. Wiltshire, New J. Phys. 9, 377 (2007); M. Sereno and P. Jetzer, Phys. Rev. D 75, 064031 (2007); P. D. Noerdlinger and V. Petrosian, Astrophys. J. 168, 1 (1971); H. Sato and K. Maeda, Prog. Theor. Phys. 70, 119 (1983); P. D. D’Eath, Phys. Rev. D 11, 1387 (1975); F. I. Cooperstock, V. Faraoni, and D. N. Vollick, Astrophys. J. 503, 61 (1998); B. Bolen, L. Bombelli, and R. Puzio, Classical Quantum Gravity 18, 1173 (2001); M. T. Busha, F. C. Adams, R. H. Wechsler, and A. E. Evrard, Astrophys. J. 596, 713 (2003); C. Gao and S. N. Zhang, Phys. Lett. B 595, 28 (2004); M. Mizony and M. Lachièze-Rey, Astron. Astrophys. 434, 45 (2005); D. Izzo and A. Rathke, arXiv:astro-ph/0504634 [J. Spacecraft and Rockets (to be published)]; F. J. Oliveira, arXiv:gr-qc/0610029 [Int. J. Theor. Phys. (to be published)]; M. Lachièze-Rey, Classical Quantum Gravity 24, 2735 (2007); J. Rosales and J. Sanchez-Gomez, arXiv:gr-qc/9810085; M. Carrera and D. Giulini, Classical Quantum Gravity 23, 7483 (2006); C. Lammerzhal and O. Preuss, arXiv:gr-qc/0604052; S. G. Turyshev and J. G. Williams, Int. J. Mod. Phys. D 16, 2165 (2007); H.-J. Fahr and M. Siewert, arXiv:gr-qc/0610034; J. G. Williams, S. G. Turyshev, and D. H. Boggs, Phys. Rev. Lett. 98, 059002 (2007); Y. V. Dumin, 98, 059001 (2007); S. Nesseris and L. Perivolaropoulos, Phys. Rev. D 70, 123529 (2004); R. H. Price, arXiv:gr-qc/0508052; A. Balaguera-Antolinez and M. Nowakowski, Classical Quantum Gravity 24, 2677 (2007); B. Mashhoon, N. Mobed, and D. Singh, 24, 5031 (2007).
  25. M. Carrera and D. Giulini, Rev. Mod. Phys. 82, 169 (2010).
  26. A. Ashtekar and B. Krishnan, Phys. Rev. Lett. 89, 261101 (2002); Phys. Rev. D 68, 104030 (2003); Living Rev. Relativity 7, 10 (2004); I. Booth, Can. J. Phys. 83, 1073 (2005); A. B. Nielsen, Gen. Relativ. Gravit. 41, 1539 (2009); M. Visser, Proc. Sci., GRandStrings (2008) 001 [arXiv:0901.4365].
  27. T. Chu, H. Pfeiffer, and M. I. Cohen, Phys. Rev. D 83, 104018 (2011).
  28. I. Ben-Dov, Phys. Rev. D 70, 124031 (2004).
  29. R. M. Wald, General Relativity (Chicago University, Chicago, 1984).
  30. R. Bousso, arXiv:hep-th/0205177.
  31. M. P. Hobson, G. Efstathiou, and A. N. Lasenby, General Relativity: An Introduction for Physicists (Cambridge University Press, Cambridge, England, 2006).
  32. A. B. Nielsen and M. Visser, Classical Quantum Gravity 23, 4637 (2006).
  33. R. W. D. Nickalls, Mathematical Gazette 77, 354 (1993).
  34. H. Arakida, Phys. Rev. D 81, 043521 (2010).
  35. C. M. Misner and D. H. Sharp, Phys. Rev. 136, B571 (1964); W. C. Hernandez and C. W. Misner, Astrophys. J. 143, 452 (1966).
  36. S. W. Hawking, J. Math. Phys. (N.Y.) 9, 598 (1968); S. A. Hayward, Phys. Rev. D 49, 831 (1994).
  37. The appearance and disappearance of pairs of apparent horizons in dynamical situations is familiar from numerical [27] and analytical [18, 28] studies of black holes.

  38. Similarly, wormholes embedded in cosmological backgrounds must expand [39].

  39. S. V. Sushkov and S.-W. Kim, Gen. Relativ. Gravit. 36, 1671 (2004); V. Faraoni and W. Israel, Phys. Rev. D 71, 064017 (2005); H. Maeda, T. Harada, and B. J. Carr, 79, 044034 (2009); I. Bochicchio and V. Faraoni, 82, 044040 (2010).
  40. D. R. Brill, G. T. Horowitz, D. Kastor, and J. Traschen, Phys. Rev. D 49, 840 (1994); H. Saida, T. Harada, and H. Maeda, Classical Quantum Gravity 24, 4711 (2007); D. N. Vollick, Phys. Rev. D 76, 124001 (2007); Y. Gong and A. Wang, Phys. Rev. Lett. 99, 211301 (2007); F. Briscese and E. Elizalde, Phys. Rev. D 77, 044009 (2008); M. Akbar and R.-G. Cai, Phys. Lett. B 635, 7 (2006); P. Wang, Phys. Rev. D 72, 024030 (2005); H. Mohseni-Sadjadi, 76, 104024 (2007); R. Di Criscienzo, M. Nadalini, L. Vanzo, and G. Zoccatelli, Phys. Lett. B 657, 107 (2007); V. Faraoni, Phys. Rev. D 76, 104042 (2007); M. Nadalini, L. Vanzo, and S. Zerbini, 77, 024047 (2008); S. A. Hayward, R. Di Criscienzo, L. Vanzo, M. Nadalini, and S. Zerbini, Classical Quantum Gravity 26, 062001 (2009); S. A. Hayward, R. Di Criscienzo, M. Nadalini, L. Vanzo, and S. Zerbini, AIP Conf. Proc. 1122, 145 (2009); R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini, and G. Zoccatelli, Phys. Lett. B 657, 107 (2007); R. Brustein, D. Gorbonos, and M. Hadad, Phys. Rev. D 79, 044025 (2009); V. Faraoni, Entropy 12, 1246 (2010).
  41. A. G. Riess et al., Astron. J. 116, 1009 (1998); 118, 2668 (1999); 560, 49 (2001); 607, 665 (2004); S. Perlmutter et al., Nature (London) 391, 51 (1998); Astrophys. J. 517, 565 (1999); J. L. Tonry et al., 594, 1 (2003); R. Knop et al., 598, 102 (2003); B. Barris et al., 602, 571 (2004).
  42. L. Amendola and S. Tsujikawa, Dark Energy: Theory and Observations (Cambridge University Press, Cambridge, England, 2010).
  43. R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).
  44. S. Nojiri and S. D. Odintsov, Phys. Rev. D 70, 103522 (2004); I. Brevik, S. Nojiri, S. D. Odintsov, and L. Vanzo, ibid.70, 043520 (2004); S. Nojiri and S. D. Odintsov, Phys. Lett. B 595, 1 (2004); E. Elizalde, S. Nojiri, and S. D. Odintsov, Phys. Rev. D 70, 043539 (2004); S. Nojiri and S. D. Odintsov, Phys. Lett. B 599, 137 (2004); K. Lake, Classical Quantum Gravity 21, L129 (2004); P. F. Gonzalez-Diaz and C. L. Siguenza, Nucl. Phys. B697, 363 (2004); R. M. Buny and D. H. Hsu, Phys. Lett. B 632, 543 (2006); D. H. Hsu, A. Jenskins, and M. B. Wise, ibid.597, 270 (2004); J. A. S. Lima and J. S. Alcaniz, ibid.600, 191 (2004); Y. Gong, B. Wang, and A. Wang, Phys. Rev. D 75, 123516 (2007); J. A. S. Lima and S. H. Pereira, ibid.78, 083504 (2008); G. Izquierdo and D. Pavon, Proceedings of the 11th Marcel Grossman Meeting, Berlin, Germany, July 2006, edited by H. Kleinert, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2008); H. M. Sadjadi, Phys. Rev. D 73, 063525 (2006).
  45. Similar situations occur in varying speed of light (VSL) cosmologies, in which the radii of primordial black holes and the Compton wavelengths of massive particle states can exceed the size of a cosmological horizon [46].

  46. J. D. Barrow, Phys. Lett. B 564, 1 (2003).
  47. V. Faraoni, V. Vitagliano, T. P. Sotiriou, and S. Liberati (unpublished).

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