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On the Possible Anisotropy of the Unruh Radiation. Part I: Massless Scalar Field in (1+1)D Space-Time

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Abstract

The Unruh effect for a massless scalar field in (1 + 1)D space-time is considered. It is shown that, under some natural assumptions like finiteness of the integration volume or finiteness of the interaction (propagation of information) speed, the Unruh effect should be anisotropic. This property is not connected with a particular detector design but is fundamental like the Unruh effect itself. This consideration can be generalized to the case of massless and massive particles in (3 + 1)D space-time. The obtained result and its further development may be important for specific applications of the Hawking-Unruh effect such as the description of black hole evaporation and motion dynamics of accelerated bodies.

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References

  1. S. W. Hawking, Nature 248, 30 (1974).

    Article  ADS  Google Scholar 

  2. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).

    Article  ADS  Google Scholar 

  3. W. G. Unruh, Phys. Rev. D 14, 870 (1976).

    Article  ADS  Google Scholar 

  4. S. A. Fulling, Phys. Rev. D 7, 2850 (1973).

    Article  ADS  Google Scholar 

  5. L. D. Landau and E. M. Lifshitz, The classical theory of fields (Pergamon Press, Oxford, 1971) (translated from the 5th revised edition of Teoriya Polia, Nauka, Moscow, 1967).

    MATH  Google Scholar 

  6. D. D. Solnyshkov, H. Flayac, and G. Malpuech, Phys. Rev. B 84, 233405 (2011).

    Article  ADS  Google Scholar 

  7. S. J. Robertson, J. Phys. B, Atomic Molecular Physics 45, 163001 (2012).

    Article  ADS  Google Scholar 

  8. D. Bermudez and U. Leonhardt, Phys. Rev. A 93, 053820 (2016).

    Article  ADS  Google Scholar 

  9. S. M. Darbinyan, K. A. Ispiryan, M. K. Ispiryan, and A. T. Margaryan, Sov. Phys. JETP Letters 51, 110 (1990).

    ADS  Google Scholar 

  10. H. C. Rosu, Grav. Cosmol. 7, 1 (2001).

    Google Scholar 

  11. L. C. B. Crispino, A. Higuchi, and G. E. A. Matsas, Rev. Mod. Phys. 80, 787 (2008).

    Article  ADS  Google Scholar 

  12. V. A. Belinskiiˇ, B. M. Karnakov, V. D. Mur, and N. B. Narozhnyiˇ, Russ. Phys. JETP Letters 65, 902 (1997).

    Article  ADS  Google Scholar 

  13. N. B. Narozhny, A. M. Fedotov, B. M. Karnakov, V. D. Mur, and V. A. Belinskii, Phys. Rev. D 65, 025004 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  14. V. S. Popov, V. D. Mur, N. B. Narozhnyi, and S. V. Popruzhenko, Russ. Phys. JETP 122, 539 (2016).

    Article  ADS  Google Scholar 

  15. U. H. Gerlach, Phys. Rev. D 27, 2310 (1983).

    Article  ADS  Google Scholar 

  16. K. Hinton, P. C. W. Davies, and J. Pfautsch, Phys. Lett. B 120, 88 (1983).

    Article  ADS  Google Scholar 

  17. W. Israel and J. M. Nester, Phys. Lett. A 98, 329 (1983).

    Article  ADS  Google Scholar 

  18. P. G. Grove and A. C. Ottewill, Class. Quantum Grav. 2, 373 (1985).

    Article  ADS  Google Scholar 

  19. N. Sanchez, Phys. Lett. A 112, 133 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  20. H. Kolbenstvedt, Phys. Lett. A 122, 292 (1987).

    Article  ADS  Google Scholar 

  21. H. Kolbenstvedt, Phys. Rev. D 38, 1118 (1988).

    Article  ADS  Google Scholar 

  22. M. B. Mensky, Theor. Math. Phys. 115, 542 (1998).

    Article  Google Scholar 

  23. J. Gine´ and M. E. McCulloch, Mod. Phys. Lett. A 31, 1650107 (2016).

    Article  ADS  Google Scholar 

  24. M. I. Katsnelson, G. E. Volovik, and M. A. Zubkov, Annals of Phys. 336, 36 (2013).

    Article  ADS  Google Scholar 

  25. R. E. Arias, H. Casini, M. Huerta, and D. Pontello, Phys. Rev. D 96, 105019 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  26. W. A. Rodrigues, Jr. and J. Vaz, Jr., arXiv: 1702.02024.

    Google Scholar 

  27. E. Kholupenko, Euro. Phys. J. Web of Conferences 191, 07006 (2018).

    Article  Google Scholar 

  28. P. C. W. Davies, Rep. Progr. Phys. 41, 1313 (1978).

    Article  ADS  Google Scholar 

  29. R. M. Wald, Living Rev. Relativity 4, 6 (2001).

    Article  ADS  Google Scholar 

  30. W. Rindler, Am. J. Phys. 34, 1174 (1966).

    Article  ADS  Google Scholar 

  31. D. Salart, A. Baas, C. Branciard, N. Gisin, and H. Zbinden, Nature 454, 861 (2008).

    Article  ADS  Google Scholar 

  32. T. G. Rudolph, Nature 454, 831 (2008).

    Article  ADS  Google Scholar 

  33. J. Yin, Y. Cao, H.-L. Yong, J.-G. Ren, H. Liang, S.-K. Liao, F. Zhou, C. Liu, Y.-P. Wu, G.-S. Pan, L. Li, N.-L. Liu, Q. Zhang, C.-Z. Peng, and J.-W. Pan, Phys. Rev. Lett. 110, 260407 (2013).

    Article  ADS  Google Scholar 

  34. V. L. Ginzburg and V. P. Frolov, Sov. Phys. Uspekhi 30, 1073 (1987).

    Article  ADS  Google Scholar 

  35. J. Franklin, Found. Phys. 43, 1489 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  36. G. F. Smoot, Physics 139. Relativity: Relativity Notes (Lectures), http://aether.lbl.gov/www/classes/p139/homework/eight.pdf (2003).

    Google Scholar 

  37. S. A. Fulling, J. D. Bouas, and H. B. Carter, Physica Scripta 90, 088006 (2015).

    Article  ADS  Google Scholar 

  38. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Pergamon Press Ltd., Oxford, 1965).

    MATH  Google Scholar 

Download references

Acknowledgment

The author is grateful to I.G. Dymnikova for a friendly review and useful remarks, to A.M. Krassilchtchikov who helped to make the manuscript clearer, and to the anonymous referee for a positive review.

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  1. Ioffe Institute, St. Petersburg, 194021, Russia

    E. E. Kholupenko

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  1. E. E. Kholupenko
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Correspondence to E. E. Kholupenko.

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Funding

The author acknowledges support from RAS Presidium program No. 3 (Ministry of Higher Education and Science project KP19-261).

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Kholupenko, E.E. On the Possible Anisotropy of the Unruh Radiation. Part I: Massless Scalar Field in (1+1)D Space-Time. Gravit. Cosmol. 25, 213–225 (2019). https://doi.org/10.1134/S0202289319030071

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  • DOI: https://doi.org/10.1134/S0202289319030071

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