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Il Nuovo Cimento B (1971-1996)

, Volume 98, Issue 1, pp 37–52 | Cite as

Bubbles of false vacuum in general relativity

  • P. F. González-Díaz
Article
  • 22 Downloads

Summary

The effects of temperature in a theory of general relativity containing higher-derivative terms modulated by a coefficient depending on lnR are studied. The theory contains a false vacuum at a value of the Higgs field close to the Planck mass, and it is shown that the false vacuum cannot exist at temperatures lower than the characteristic mass of the theory. The homogeneous field equations are solved for the case of a static, spherically symmetric gravitational system, finding that the solution corresponds exactly to the Schwarzschild line element. Also considered is the process of temperature-dependent phase transition in the framework of this theory. Reasons are given which support the proposal that black holes could be considered as bubbles of false vacuum, ending with some arguments that seem to prevent the existence of black holes.

PACS.04.90

Other topics in relativity and gravitation 

PACS.04.20.Jb.

Solutions to equations 

PACS.04.60

Quantum theory of gravitation 

Пузыри ложного вакуума в общей теории относительности

Резюме

Исследуются температурные эффекты в общей теории относительности, содержащей члены высших производных с коэффициентами, зависящими от lnR. Указанная теория содержит ложный вакуум при значении поля Хиггса, близком к массе Планка. Показывается, что ложный вакуум не может существовать при температурах, ниже характеристической массы теопии Уравнения для однородного поля решаются в случае статической сферически симметричной гравитационной системы. Получается, что решение точно соответствует линейному элементу Шварцшильда. В рамках предложенной теории также рассматривают процесс фазового перехода, зависящего от температуры. Приводятся причины, которые подтверждают предположение, что черные дыры можно рассмтривать как пузыри ложного вакуума. Указываются некоторые аргументы, которые не допускают существование черных дыр.

Riassunto

Si studiano gli effetti della temperatura in una teoria della relatività generale che contiene termini a derivata piú alta modulati da un coefficiente dipendente da lnR. La teoria contiene un falso vuoto ad un valore del campo di Higgs vicino alla massa di Planck e si mostra che il falso vuoto non può esistere a temperature piú basse della massa caratteristica della teoria. Le equazioni di campo omogenee sono risolte per il caso di un sistema gravitazionale statico a simmetria sferica, e si trova che la soluzione corrisponde esattamente all'elemento di linea di Schwarzschild. Si considera anche il processo della transizione di fase che dipende dalla temperatura nel sistema di questa teoria. Si forniscono ragioni a favore della proposta che i buchi neri possano essere considerati come bolle di falso vuoto, concludendo con alcuni argomenti che sembrano prevenire l'esistenza di buchi neri.

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References

  1. (1).
    C. J. Isham: inQuantum Gravity 2:A Second Oxford Symposium, edited byC. J. Isham, R. Penrose andD. W. Sciama (Clarendon, Oxford, 1981).Google Scholar
  2. (2).
    K. S. Stelle:Phys. Rev. D,16, 953 (1977).MathSciNetADSCrossRefGoogle Scholar
  3. (3).
    J. B. Hartle andB. L. Hu:Phys. Rev. D,20, 1772 (1979);J. B. Hartle:Phys. Rev. D,22, 2091 (1980);A. A. Starobinskii:Phys. Lett. B,91, 99 (1978);V. T. Gurovich andA. A. Starobinskii:Sov. Phys. JETP,50, 844 (1979);V. I. Ginzburg, D. A. Kirzhnits andA. A. Lyubushin:Sov. Phys. JETP,33, 242 (1971);P. Havas:Gen. Rel. Grav.,8, 631 (1977).MathSciNetADSCrossRefGoogle Scholar
  4. (4).
    M. V. Fishetti, J. H. Hartle andB. L. Hu:Phys. Rev. D,20, 1757 (1979).MathSciNetADSCrossRefGoogle Scholar
  5. (5).
    E. Sezgin andP. van Nieuwenhuizen:Phys. Rev. D,21, 3269 (1980);E. T. Tomboulis: inQuantum Theory of Gravity, edited byS. M. Christensen (Hilger, Bristol, 1984).MathSciNetADSCrossRefGoogle Scholar
  6. (6).
    J. Julve andM. Tonin:Nuovo Cimento B,46, 137 (1978).MathSciNetADSCrossRefGoogle Scholar
  7. (7).
    A. Salam andJ. Strathdee:Phys. Rev. D,18, 4480 (1978).MathSciNetADSCrossRefGoogle Scholar
  8. (8).
    E. T. Tomboulis:Phys. Lett. B,70, 361 (1977).;97, 77 (1980).ADSCrossRefGoogle Scholar
  9. (9).
    G. T. Horowitz andR. M. Wald:Phys. Rev. D,17, 414 (1978).MathSciNetADSCrossRefGoogle Scholar
  10. (10).
    P. F. González-Díaz:Phys. Rev. D,33, 1835 (1986).MathSciNetADSCrossRefGoogle Scholar
  11. (11).
    P. F. González-Díaz:Phys. Lett. B,151, 405 (1985);Nuovo Cimento B,90, 65 (1985).ADSCrossRefGoogle Scholar
  12. (12).
    F. Lucchin, S. Matarrese andM. D. Pollock:Phys. Lett. B,167, 163 (1986).ADSCrossRefGoogle Scholar
  13. (13).
    M. D. Pollock:Phys. Lett. B,167, 301 (1986).MathSciNetADSCrossRefGoogle Scholar
  14. (14).
    M. D. Pollock:Primordial inflation with a broken symmetry theory of gravity, International Centre for Theoretical Physics, Trieste, ICTP-preprint (1985).Google Scholar
  15. (15).
    P. F. González-Díaz:Phys. Lett. B,159, 19 (1985).ADSCrossRefGoogle Scholar
  16. (16).
    P. F. González-Díaz:Phys. Lett. B,176, 29 (1986).ADSCrossRefGoogle Scholar
  17. (17).
    A. S. Eddington:Relativitätstheorie in mathematischer Bedhandlung (J. Springer, Berlin, 1925);C. Lanczos:Z. Phys.,73, 147 (1932);Ann. Math. (Leipzig),39, 842 (1938);H. Buchdahl:Nuovo Cimento,123, 141 (1962);C. Gregory:Phys. Rev.,72, 72 (1947).Google Scholar
  18. (18).
    E. Pechlaner andR. Sexl:Commun. Math. Phys.,2, 165 (1966).MathSciNetADSCrossRefMATHGoogle Scholar
  19. (19).
    G. T. Horowitz: inQuantum Gravity 2. A Second Oxford Symposium, edited byC. J. Isham, R. Penrose andD. W. Sciama (Clarendon, Oxford, 1981).Google Scholar
  20. (20).
    S. Adler:Phys. Rev. Lett.,44, 1567 (1980);A. D. Linde:Phys. Lett. B,93, 394 (1980);P. C. W. Davies:Phys. Lett. B,101, 399 (1981);110, 111 (1982).MathSciNetADSCrossRefGoogle Scholar
  21. (21).
    L. Dolan andR. Jackiw:Phys. Rev. D,9, 3320 (1974).ADSCrossRefGoogle Scholar
  22. (22).
    D. A. Kirzhnits andA. D. Linde:Sov. Phys. JETP,40, 628 (1975);A. D. Linde:Rep. Prog. Phys.,42, 389 (1979).ADSGoogle Scholar
  23. (23).
    A. Apelblat:Table of Definite and Indefinite Integrals (Elsevier Science Publ. Co., Amsterdam, 1983).Google Scholar
  24. (24).
    See, for example,C. A. Mead:Phys. Rev. B,135, 849 (1964);H.-H. Borzeszkowski andH.-J. Treder:Ann. Phys. (Leipzig),40, 287 (1983).MathSciNetADSCrossRefGoogle Scholar
  25. (25).
    T. Padmanabham:Ann. Phys. (N. Y.),165, 38 (1985).ADSCrossRefGoogle Scholar
  26. (26).
    J. A. Wheeler:Ann. Phys. (N. Y.),2, 604 (1957);C. W. Misner, K. S. Thorne andJ. A. Wheeler:Gravitation (Freeman, San Francisco, Cal., 1973).ADSCrossRefMATHGoogle Scholar
  27. (27).
    We have only written the term depending explicitly on the metricg; other terms in the integral can be ignored in our discussion.Google Scholar
  28. (28).
    K. S. Stelle:Gen. Rel. Grav.,9, 353 (1978).MathSciNetADSCrossRefGoogle Scholar
  29. (29).
    G. W. Gibbons andB. F. Whiting:Nature (London),291, 636 (1981).ADSCrossRefGoogle Scholar
  30. (30).
    E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge andS. H. Aronson:Phys. Rev. Lett.,56, 3 (1986).ADSCrossRefGoogle Scholar
  31. (31).
    S. H. Aronson, G. J. Bock, H. Y. Cheng andE. Fischbach:Phys. Rev. Lett.,48, 1306 (1982);Phys. Rev. D,28, 476, 495 (1983);E. Fischbach, H. Y. Cheng, S. H. Aronson andG. J. Bock:Phys. Lett. B,116, 73 (1982).ADSCrossRefGoogle Scholar
  32. (32).
    See, for example,F. D. Stacey, G. J. Tuck, G. I. Moore, S. C. Holding, B. D. Goodwin andR. Zhou: University of Queensland preprint (1986).Google Scholar
  33. (33).
    E. Fischbach, D. Sudarsky, A. Szafer, C. Talmadge andS. H. Aronson:A New Force in Nature?, paper presentedThe II Conference on Intersections between Particle and Nuclear Physics, Canada, 1986.Google Scholar
  34. (34).
    W. Thirring:Ann. Phys. (N. Y.),16, 91 (1961).ADSCrossRefGoogle Scholar
  35. (35).
    L. D. Landau andE. M. Lifshitz:Teoría Clásica de Campos (Reverté, Barcelona, 1966).Google Scholar
  36. (36).
    S. Weinberg:Gravitation and Cosmology (John Wiley and Sons, Inc., New York, N. Y., 1972).Google Scholar
  37. (37).
    E. L. Ince:Integración de Ecuaciones Diferenciales Ordinarias (Editorial Dossat, S. A., Madrid, 1963).Google Scholar
  38. (38).
    For a review, seeA. D. Linde:Nucl. Phys. B,216, 421 (1983).MathSciNetADSCrossRefGoogle Scholar
  39. (39).
    See, for example,E. Witten:Nucl. Phys. B,177, 477 (1981).ADSCrossRefGoogle Scholar
  40. (40).
    L. F. Abbott:Nucl. Phys. B,185, 233 (1981).ADSCrossRefGoogle Scholar
  41. (41).
    A. Guth andS.-H. Tye:Phys. Rev. Lett.,44, 631, 963 (1980);M. Sher:Phys. Rev. D,22, 2989 (1980);Nucl. Phys. B,183, 77 (1981);P. Steinhardt:Nucl. Phys. B,179, 492 (1981).ADSCrossRefGoogle Scholar
  42. (42).
    S. Coleman:Phys. Rev. D,15, 2929 (1977);C. G. Callan andS. Coleman:Phys. Rev. D,16, 1762 (1977).ADSCrossRefGoogle Scholar
  43. (43).
    S. Coleman andF. DeLuccia:Phys. Rev. D.,21, 3305 (1980).MathSciNetADSCrossRefGoogle Scholar
  44. (44).
    L. F. Abbott andM. B. Wise:Am. J. Phys.,49, 37 (1981).MathSciNetADSCrossRefGoogle Scholar
  45. (45).
    B. B. Mandelbrot:The Fractal Geometry of Nature (Freeman, New York N. Y., 1983).Google Scholar
  46. (46).
    D. N. Page:Phys. Rev. D,13, 198 (1976).ADSCrossRefGoogle Scholar
  47. (47).
    S. W. Hawking: inAstrophysical Cosmology, Proceedings of the Study Week on Cosmology and Fundamental Physics, edited byH. A. Brüch, H. A. Coyne andM. S. Longair (P.A.S. Scripta Varia, Vatican City, 1982), p. 563.Google Scholar
  48. (48).
    S. W. Hawking:The density matrix of the universe, DAMTP preprint, University of Cambridge (1986);J. B. Hartle:Initial conditions and quantum cosmology, University of California preprint (1986).Google Scholar
  49. (49).
    M. K. Crawford, R. Genzel, A. I. Harris, D. T. Jaffe, J. H. Lacy, J. B. Lugten, E. Serabyn andC. H. Townes:Nature (London),315, 467 (1985).ADSCrossRefGoogle Scholar
  50. (50).
    S. W. Hawking andI. G. Moss:Phys. Lett. B,110, 35 (1983).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1987

Authors and Affiliations

  • P. F. González-Díaz
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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