Skip to main content
SpringerLink
Log in

Type-II Weyl Semimetal versus Gravastar

  • MULTIDISCIPLINARY
  • Published:
JETP Letters Aims and scope Submit manuscript

The boundary between the type I and type II Weyl semimetals serves as the event horizon for the “relativistic” fermions. The interior of the black hole is represented by the type II Weyl semimetal, where the Fermi surface is formed. The process of the filling of the Fermi surface by electrons results in the relaxation inside the horizon. This leads to the Hawking radiation and to the reconstruction of the interior vacuum state. After the Fermi surface is fully occupied, the interior region reaches the equilibrium state, for which the Hawking radiation is absent. If this scenario is applicable to the real black hole, then the final state of the black hole will be the dark energy star with the event horizon. Inside the event horizon one would have de Sitter spacetime, which is separated from the event horizon by the shell of the Planck length width. Both the de Sitter part and the shell are made of the vacuum fields without matter. This is distinct from the gravastar, in which the matter shell is outside the “horizon,” and which we call the type I gravastar. However, this is similar to the other type of the vacuum black hole, where the shell is inside the event horizon, and which we call the type II gravastar. We suggest to study the vacuum structure of the type II gravastar using the q-theory, where the vacuum variable is the 4-form field introduced for the phenomenological description of the quantum vacuum.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. F. Soltani, C. Rovelli, and P. Martin-Dussaud, Phys. Rev. D 104, 066015 (2021); arXiv: 2105.06876.

  2. G. Chapline, E. Hohlfeld, R. B. Laughlin, and D. I. Santiago, Int. J. Mod. Phys. A 18, 3587 (2003).

    Article  ADS  Google Scholar 

  3. G. E. Volovik, Phys. Rep. 351, 195 (2001); gr-qc/0005091.

    Article  ADS  MathSciNet  Google Scholar 

  4. M. J. Duff and P. van Nieuwenhuizen, Phys. Lett. B 94, 179 (1980).

    Article  ADS  Google Scholar 

  5. A. Aurilia, H. Nicolai, and P. K. Townsend, Nucl. Phys. B 176, 509 (1980).

    Article  ADS  Google Scholar 

  6. S. W. Hawking, Phys. Lett. B 134, 403 (1984).

    Article  ADS  Google Scholar 

  7. G. E. Volovik, JETP Lett. 104, 645 (2016); arXiv: 1610.00521.

  8. W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).

    Article  ADS  Google Scholar 

  9. G. E. Volovik and K. Zhang, J. Low Temp. Phys. 189, 276 (2017); arXiv: 1604.00849.

  10. L. Liang and T. Ojanen, Phys. Rev. Res. 1, 032006(R) (2019).

  11. K. Hashimoto and Y. Matsuo, Phys. Rev. B 102, 195128 (2020).

  12. Y. Kedem, E. J. Bergholtz, and F. Wilczek, Phys. Rev. Res. 2, 043285 (2020).

  13. C. de Beule, S. Groenendijk, T. Meng, and T. L. Schmidt, arXiv: 2106.14595.

  14. D. Sabsovich, P. Wunderlich, V. Fleurov, D. I. Pikulin, R. Ilan, and T. Meng, arXiv: 2106.14553.

  15. C. Morice, A. G. Moghaddam, D. Chernyavsky, J. van Wezel, and J. van den Brink, Phys. Rev. Res. 3, L022022 (2021).

  16. G. E. Volovik and M. A. Zubkov, Nucl. Phys. B 881, 514 (2014); arXiv: 1402.5700.

    Article  ADS  Google Scholar 

  17. M. Zahid Hasan, G. Chang, I. Belopolski, G. Bian, S.‑Y. Xu, and J.-X. Yin, Nat. Rev. Mater. 6, 784 (2021). https://doi.org/10.1038/s41578-021-00301-3

  18. P. Painlevé, C. R. Acad. Sci. (Paris) 173, 677 (1921).

    Google Scholar 

  19. A. Gullstrand, Arkiv. Mat. Astron. Fys. 16, 1 (1922).

    Google Scholar 

  20. G. E. Volovik, Phys. Lett. A 142, 282 (1989).

    Article  ADS  Google Scholar 

  21. W. V. Liu and F. Wilczek, Phys. Rev. Lett. 90, 047002 (2003).

  22. D. F. Agterberg, P. M. R. Brydon, and C. Timm, Phys. Rev. Lett. 118, 127001 (2017).

  23. P. M. R. Brydon, D. F. Agterberg, H. Menke, and C. Timm, Phys. Rev. B 98, 224509 (2018).

  24. C. Timm and A. Bhattacharya, arXiv: 2107.01839.

  25. V. B. Eltsov, T. Kamppinen, J. Rysti, and G. E. Volovik, arXiv: 1908.01645.

  26. S. Sumita, T. Nomoto, K. Shiozaki, and Y. Yanase, Phys. Rev. B 99, 134513 (2019).

  27. S. Autti, J. T. Mäkinen, J. Rysti, G. E. Volovik, V. V. Zavjalov, and V. B. Eltsov, Phys. Rev. Res. 2, 033013 (2020); arXiv: 2002.11492.

  28. H. Oh, D. Agterberg, and E.-G. Moon, arXiv: 2105.09317.

  29. N. B. Kopnin and G. E. Volovik, JETP Lett. 67, 140 (1998); cond-mat/9712187.

    Article  ADS  Google Scholar 

  30. T. A. Jacobson and G. E. Volovik, Phys. Rev. D 58, 064021 (1998); cond-mat/9801308.

  31. G. E. Volovik, JETP Lett. 113, 602 (2021); arXiv: 2104.01013.

  32. G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).

    MATH  Google Scholar 

  33. P. Hořava, Phys. Rev. Lett. 95, 016405 (2005).

  34. G. E. Volovik, JETP Lett. 46, 98 (1987).

    ADS  Google Scholar 

  35. C. Sims, Condens. Matter 6, 18 (2021).

    Article  Google Scholar 

  36. M. Zubkov, Universe 4, 135 (2018).

    Article  ADS  Google Scholar 

  37. P. Huhtala and G. E. Volovik, J. Exp. Theor. Phys. 94, 853 (2002); gr-qc/0111055.

    Article  ADS  MathSciNet  Google Scholar 

  38. M. A. Zubkov, Mod. Phys. Lett. A 33, 1850047 (2018).

  39. M. Lewkowicz and M. Zubkov, Symmetry 11, 1294 (2019).

    Article  Google Scholar 

  40. F. D’Ambrosio, M. Christodoulou, P. Martin-Dussaud, C. Rovelli, and F. Soltani, Phys. Rev. D 103, 106014 (2021).

  41. G. E. Volovik, Mod. Phys. Lett. A 36, 2150117 (2021); arXiv: 2103.10954.

  42. P. O. Mazur and E. Mottola, arXiv: gr-qc/0109035.

  43. P. O. Mazur and E. Mottola, Proc. Natl. Acad. Sci. U. S. A. 101, 9545 (2004).

    Article  ADS  Google Scholar 

  44. M. Visser and D. L. Wiltshire, Clas. Quantum Grav. 21, 1135 (2004).

    Article  ADS  Google Scholar 

  45. F. R. Klinkhamer and G. E. Volovik, Phys. Lett. A 347, 8 (2005); gr-qc/0503090.

    Article  ADS  MathSciNet  Google Scholar 

  46. V. P. Frolov, M. A. Markov, and V. F. Mukhanov, Phys. Rev. D 41, 383 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  47. I. Dymnikova, Gen. Relat. Grav. 24, 235 (1992).

    Article  ADS  Google Scholar 

  48. I. Dymnikova, Class. Quantum Grav. 19, 725 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  49. I. Dymnikova, Universe 6, 101 (2020).

    Article  ADS  Google Scholar 

  50. H. Maeda, arXiv: 2107.04791.

  51. A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, J. High Energy Phys. 02, 06202 (2013).

    Google Scholar 

  52. G. ’t Hooft, Found. Phys. 47, 1503 (2017); arXiv: 1612.08640.

  53. V. Cardoso and P. Pani, Living. Rev. Relat. 22, 4 (2019).

    Article  ADS  Google Scholar 

  54. G. ’t Hooft, arXiv: 2106.11152.

  55. I. Antoniou, arXiv: 2010.05354.

  56. D. Gerosa and M. Fishbach, arXiv: 2105.03439.

  57. F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 77, 085015 (2008); arXiv: 0711.3170.

  58. F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 78, 063528 (2008); arXiv: 0806.2805 [gr-qc].

  59. G. E. Volovik, arXiv: 2011.06466.

  60. D. Benisty, E. I. Guendelman, A. Kaganovich, E. Nissimov, and S. Pacheva, Eur. Phys. J. Plus 136, 46 (2021).

    Article  Google Scholar 

  61. F. R. Klinkhamer and G. E. Volovik, Mod. Phys. Lett. A 32, 1750103 (2017); arXiv: 1609.03533.

  62. F. R. Klinkhamer and G. E. Volovik, JETP Lett. 105, 74 (2017); arXiv: 1612.02326.

  63. Ya. B. Zel’dovich, Sov. Phys. JETP 14, 1143 (1962).

    Google Scholar 

  64. P. Beltracchi, P. Gondolo, and E. Mottola, arXiv: 2107.00762.

  65. Ya. B. Zel’dovich, JETP Lett. 14, 180 (1971).

    ADS  Google Scholar 

  66. Ya. B. Zel’dovich, Sov. Phys. JETP 35, 1085 (1971).

    ADS  Google Scholar 

  67. A. A. Starobinskii, Sov. Phys. JETP 37, 28 (1973).

    ADS  Google Scholar 

  68. H. Takeuchi, M. Tsubota, and G. E. Volovik, J. Low Temp. Phys. 150, 624 (2008); arXiv: 0710.2178.

    Article  ADS  Google Scholar 

Download references

ACKNOWLEDGMENTS

I am grateful to M. Zubkov for discussions.

Funding

This work was supported by the European Research Council (grant agreement no. 694248, European Union’s Horizon 2020 research and innovation programme).

Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076, Aalto, Finland

    G. E. Volovik

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow region, Russia

    G. E. Volovik

Authors
  1. G. E. Volovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. E. Volovik.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Volovik, G.E. Type-II Weyl Semimetal versus Gravastar. Jetp Lett. 114, 236–242 (2021). https://doi.org/10.1134/S0021364021160013

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364021160013

Search

Navigation