Skip to main content
SpringerLink
Log in

Trapped Ghosts as Sources for Wormholes and Regular Black Holes. The Stability Problem

  • Chapter
  • First Online:
Wormholes, Warp Drives and Energy Conditions

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 189))

Abstract

The chapter briefly reviews the properties of static, spherically symmetric configurations of general relativity with a minimally coupled scalar field \(\phi \) whose kinetic energy is negative in a restricted (strong-field) region of space and positive outside it. This “trapped ghost” concept may in principle explain why no ghosts are observed under usual, weak-field conditions. The configurations considered are wormholes and regular black holes without a center, in particular, black universes (black holes with an expanding cosmology beyond the event horizon). Spherically symmetric perturbations of these objects are considered, and it is stressed that, due to the universal shape of the effective potential near a transition surface from canonical to phantom behavior of the scalar field, such surfaces restrict the possible perturbations and play a stabilizing role.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Our conventions are: the metric signature \((+\ -\ -\ -)\), the curvature tensor \(R^{\sigma }{}_{\mu \rho \nu } = \partial _\nu \varGamma ^{\sigma }_{\mu \rho }-\ldots ,\ R_{\mu \nu }= R^{\sigma }{}_{\mu \sigma \nu }\), so that the Ricci scalar \(R > 0\) for de Sitter spacetime and the matter-dominated cosmological epoch; the sign of \(T_\mu ^\nu \) such that \(T^0_0\) is the energy density, and the system of units \(8\pi G = c = 1\).

  2. 2.

    In what follows we will use different radial coordinates, to be denoted by different letters:

           u — a general notation,

           x — quasiglobal, such that \(\alpha = -\gamma \),

           y — harmonic, such that \(\alpha = 2\beta + \gamma \),

           z — “tortoise,” such that \(\alpha = \gamma \).

  3. 3.

    For a detailed description of the properties of Fisher and anti-Fisher solutions see [8, 13, 38, 39] and references therein. Let us here only mention that the metric (7.14) describes wormholes [5, 6] if \(k < 0\), which is only possible with negative h; one flat spatial infinity then corresponds to \(y=0\), the other one to \(y = \pi /|k|\).

References

  1. Schwarzschild K. Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften. 1916;1:189–96.

    MATH  Google Scholar 

  2. Flamm L. Beitráge zur Einsteinschen Gravitationstheorie. Phys Z. 1916;17:48.

    MATH  Google Scholar 

  3. Morris MS, Thorne KS. Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity. Am J Phys. 1988;56:395.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Hochberg D, Visser M. Geometric structure of the generic static traversable wormhole throat. Phys Rev D. 1997;56:4745.

    Article  ADS  MathSciNet  Google Scholar 

  5. Bronnikov KA. Scalar-tensor theory and scalar charge. Acta Phys Pol B. 1973;4:251.

    MathSciNet  Google Scholar 

  6. Ellis H. Ether flow through a drainhole – a particle model in general relativity. J Math Phys. 1973;14:104.

    Article  ADS  MathSciNet  Google Scholar 

  7. Bronnikov KA. Spherically symmetric false vacuum: no-go theorems and global structure. Phys Rev D. 2001;64:064013.

    Article  ADS  MathSciNet  Google Scholar 

  8. Sushkov SV, Zhang Y-Z. Scalar wormholes in cosmological setting and their instability. Phys Rev D. 2008;77:024042.

    Article  ADS  Google Scholar 

  9. Bronnikov KA, Starobinsky AA. No realistic wormholes from ghost-free scalar-tensor phantom dark energy. JETP Lett. 2007;85:1.

    Article  ADS  Google Scholar 

  10. Bronnikov KA, Starobinsky AA. Once again on thin-shell wormholes in scalar-tensor gravity. Mod Phys Lett A. 2009;24:1559.

    Article  ADS  MATH  Google Scholar 

  11. Bronnikov KA, Skvortsova MV, Starobinsky AA. Notes on wormhole existence in scalar-tensor and F(R) gravity. Grav Cosmol. 2010;16:216.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Lobo FSN. Exotic solutions in general relativity: traversable wormholes and warp drive spacetimes. In: Classical and Quantum Gravity Research. Nova Sci. Pub.; 2008. pp. 1–78

    Google Scholar 

  13. Bronnikov KA, Rubin SG. Black holes, cosmology, and extra dimensions. World Scientific; 2012.

    Google Scholar 

  14. Bronnikov KA. Scalar-tensor gravity and conformal continuations. J Math Phys. 2002;43:6096–115.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Bronnikov KA, Galiakhmetov AM. Wormholes without exotic matter in Einstein-Cartan theory. Grav Cosmol. 2015;21:283.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Bronnikov KA, Galiakhmetov AM. Wormholes and black universes without phantom fields in Einstein-Cartan theory. Phys Rev D. 2016;94:124006.

    Article  ADS  Google Scholar 

  17. Dotti Gustavo, Oliva Julio, Troncoso Ricardo. Static wormhole solution for higher-dimensional gravity in vacuum. Phys Rev D. 2007;75:024002.

    Article  ADS  Google Scholar 

  18. Harko T, Lobo FSN, Mak MK, Sushkov SV. Gravitationally modified wormholes without exotic matter.

    Google Scholar 

  19. Bronnikov KA, Kim S-W. Possible wormholes in a brane world. Phys Rev D. 2003;67:064027.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Korolev RV, Sushkov SV. Exact wormhole solutions with nonminimal kinetic coupling. arXiv: 1408.1235.

  21. Bronnikov KA, Sushkov SV. Trapped ghosts: a new class of wormholes. Quantum Grav. 2010;27:095022.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Kroger H, Melkonian G, Rubin SG. Cosmological dynamics of scalar field with non-minimal kinetic term. Gen Rel Grav. 2004;36:1649.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Bronnikov KA, Fabris JC. Regular phantom black holes. Phys Rev Lett. 2006;96:251101.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Bronnikov KA, Melnikov VN, Dehnen H. Regular black holes and black universes. Gen Rel Grav. 2007;39:973.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Bolokhov SV, Bronnikov KA, Skvortsova MV. Magnetic black universes and wormholes with a phantom scalar. Class Quantum Grav. 2012;29:245006.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Bronnikov KA, Donskoy EV. Black universes with trapped ghosts. Grav Cosmol. 2011;17:176–80.

    Article  ADS  MATH  Google Scholar 

  27. Bronnikov KA, Donskoy EV, Korolyov P. Magnetic wormholes and black universes with trapped ghosts. Vestnik RUDN No. 2013;2:139–49.

    Google Scholar 

  28. Bronnikov KA, Khodunov AV. Scalar field and gravitational instability. Gen Rel Grav. 1979;11:13.

    Article  ADS  MathSciNet  Google Scholar 

  29. Bronnikov KA, Grinyok SV. Instability of wormholes with a nonminimally coupled scalar field. Grav Cosmol. 2001;7:297.

    ADS  MathSciNet  MATH  Google Scholar 

  30. Bronnikov KA, Grinyok SV. Conformal continuations and wormhole instability in scalar-tensor gravity. Grav Cosmol. 2004;10:237.

    ADS  MathSciNet  MATH  Google Scholar 

  31. Shinkai Hisa-aki, Hayward Sean A. Fate of the first traversible wormhole: black-hole collapse or inflationary expansion. Phys Rev D. 2002;66:044005.

    Article  ADS  MathSciNet  Google Scholar 

  32. Gonzalez JA, Guzman FS, Sarbach O. Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis. Class Quantum Grav. 2009;26:015010.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Gonzalez JA, Guzman FS, Sarbach O. On the instability of charged wormholes supported by a ghost scalar field. Phys Rev D. 2009;80:024023.

    Article  ADS  MATH  Google Scholar 

  34. Bronnikov KA, Fabris JC, Zhidenko A. On the stability of scalar-vacuum space-times. Eur Phys J C. 2011;71(11):1791.

    Article  ADS  Google Scholar 

  35. Bronnikov KA, Konoplya RA, Zhidenko A. Instabilities of wormholes and regular black holes supported by a phantom scalar field. Phys Rev D. 2012;86:024028.

    Article  ADS  Google Scholar 

  36. Fisher IZ. Scalar mesostatic field with regard for gravitational effects. Zh Eksp Teor Fiz. 1948;18:636.

    Google Scholar 

  37. Bergmann O, Leipnik R. Space-time structure of a static spherically symmetric scalar field. Phys Rev. 1957;107:1157.

    Article  ADS  MathSciNet  Google Scholar 

  38. Bronnikov KA, Chernakova MS, Fabris JC, Pinto-Neto N, Rodrigues ME. Cold black holes and conformal continuations. Int J Mod Phys D. 2008;17:25–42.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Bronnikov KA, Chervon SV, Sushkov SV. Wormholes supported by chiral fields. Grav Cosmol. 2009;15:241.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Bronnikov KA, Korolyov PA. Magnetic wormholes and black universes with invisible ghosts. Grav Cosmol. 2015;21:157–65.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Bronnikov KA, Lipatova LN, Novikov ID, Shatskiy AA. Example of a stable wormhole in general relativity. Grav Cosmol. 2013;19:269.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Bronnikov KA, Clément G, Constantinidis CP, Fabris JC. Cold scalar-tensor black holes: causal structure, geodesics, stability. Grav Cosmol. 1998;4:128.

    ADS  MathSciNet  MATH  Google Scholar 

  43. Brandenberger RH, Feldman HA, Mukhanov VF. Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions. Phys Rep. 1992;215:203.

    Article  ADS  MathSciNet  Google Scholar 

  44. Ishibashi A, Kodama H. Stability of higher-dimensional Schwarzschild black holes. Prog Theor Phys. 2003;110:901.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Ishibashi A, Kodama H. Perturbations and stability of static black holes in higher dimensions. Prog Theor Phys Suppl. 2011;189:165.

    Article  ADS  MATH  Google Scholar 

  46. McFadden Paul L, Turok Neil G. Effective theory approach to brane world black holes. Phys Rev D. 2005;71:086004.

    Article  ADS  MathSciNet  Google Scholar 

  47. Bocharova N, Bronnikov K, Melnikov V. On an exact solution of the Einstein-scalar field equations. Vestn Mosk Univ Fiz Astron. 1970;6:706.

    Google Scholar 

  48. Bekenstein JD. Exact solutions of Einstein–conformal scalar equations. Ann Phys (NY). 1974;82:535.

    Article  ADS  MathSciNet  Google Scholar 

  49. Landau LD, Lifshits EM. Quantum mechanics. non-relativistic theory. 3rd ed. Oxford: Pergamon; 1991.

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Russian Foundation for Basic Research grant 16-02-00602.

Author information

Authors and Affiliations

  1. Center of Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya St. 46, Moscow, 119361, Russia

    Kirill A. Bronnikov

  2. Institute of Gravitation and Cosmology, PFUR, Miklukho-Maklaya St. 6, Moscow, 117198, Russia

    Kirill A. Bronnikov

  3. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Highway 31, Moscow, 115409, Russia

    Kirill A. Bronnikov

Authors
  1. Kirill A. Bronnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kirill A. Bronnikov .

Editor information

Editors and Affiliations

  1. Departamento de Física da FCUL , Lisboa, Grande Lisboa, Portugal

    Francisco S. N. Lobo

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Bronnikov, K.A. (2017). Trapped Ghosts as Sources for Wormholes and Regular Black Holes. The Stability Problem. In: Lobo, F. (eds) Wormholes, Warp Drives and Energy Conditions. Fundamental Theories of Physics, vol 189. Springer, Cham. https://doi.org/10.1007/978-3-319-55182-1_7

Download citation

Publish with us

Policies and ethics

Search

Navigation