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Type-D solutions of the Einstein and Born-Infeld nonlinear-electrodynamics equations

РещениеD типа уравнений нелинейной электродинамики Эйнщтейна и Борна-йнфельда

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Il Nuovo Cimento B (1971-1996)

Summary

All type-D solutions of the Einstein-Born-Infeld equations for an algebraically general nonlinear electromagnetic field aligned along the Debever-Penrose directions are determined. The most general classes of solutions are nonlinear electromagnetic generalizations of the NUT-\(\tilde B\)(+) and anti-NUT-\(\tilde B\)(−) metrics. Subfamilies of solutions are the generalized Reissner-Nordstrom and anti-Reissner-Nordstrom metrics. The most special solution in the Bertotti-Robinson metric interpreted from the viewpoint of nonlinear electrodynamics.

Riassunto

Tutte le equazioni di tipoD delle equazioni di Einstein-Born-Infeld per un campo elettromagnetico algebricamente generale non lineare allineato lungo le direzioni di Debever-Penrose sono determinate. Le classi piú generali i soluzioni sono generalizzazioni elettromagnetiche non lineari delle metriche NUT\(\tilde B\)(+) e dell’anti-NUT\(\tilde B\)(−). Sottofamiglie di soluzioni sono le metriche generalizzate di Reissner-Nordstrom e anti Reissner-Nordstrom. La soluizione piú speciale è la metrica di Bertotti-Robinson interpretata dal punto di vista dell’elettrodinamica non lineare.

Резюме

Определяются все решенияD типа уравнений Эйнштейна-Борна-Инфельда для алтебраически общего нелинейного электроматнитного поля, орнентированного вдоль направлений Дебевера-Пенроуза. Наиболее общие классы решений являются нелинейными электромагнтными обобщениями NUT-\(\tilde B\)(+) и анти-NUT-\(\tilde B\)(−) метрик. Подсемейства решений представляют обобщенные метрики Рейснера-Норстрема и анти-Рейснера-Нордстрема. Наиболее специальное решение представляет метрику Бертотти-Робинсона, которая интерпретируется с точки зрения нелинейной электродинамики.

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References

  1. M. Born:Nature (London),132, 282 (1933);Proc. R. Soc. London, Ser. A,143, 410 (1934);M. Born andL. Infeld:Nature (London),132, 970, 1004 (1933);Proc. R. Soc. London, Ser. A,144, 425 (1934);147, 522 (1934);150, 141 (1935);C. R. Acad. Sci.,199, 1297 (1934);L. Infeld:Proc. Cambridge Philos. Soc.,32, 127 (1936);33, 70 (1937);Nature (London),137, 658 (1936).

    Article  ADS  Google Scholar 

  2. J. Slavik: Doctoral Thesis (1976), Institute of Theoretical Physics of the University of Warszawa, Poland.

  3. R. Pellicer andR. J. Torrence:J. Math. Phys. (N. Y.),10, 1718 (1969).

    Article  ADS  Google Scholar 

  4. L. E. Morales:Nuovo Cimento B,68, 55 (1982).

    Article  ADS  Google Scholar 

  5. J. F. Plebański:Lectures of Nonlinear Electrodynamics, monography of the Niels Bohr Institute Nordita, Copenhagen (1968).

  6. S. Alarcón G., A. L. Dudley andJ. F. Plebański:J. Math. Phys. (N. Y.),22, 2835 (1981).

    Article  ADS  Google Scholar 

  7. B. Bertotti:Phys. Rev.,116, 1331 (1959).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. I. Robinson:Bull. Acad. Pol. Sci. Serv. Math. Phys.,7, 352 (1959).

    Google Scholar 

  9. H. Reissner:Ann. Phys. (Leipzig),50, 106 (1916).

    Article  ADS  Google Scholar 

  10. C. Nordstrom:Proc. K. Ned. Akad. Wet.,20, 1238 (1918).

    Google Scholar 

  11. T. Newman, L. Tamburino andT. Unti:J. Math. Phys., (N. Y.),4, 915 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. B. Carter:Commun. Math. Phys.,10, 280 (1968).

    MATH  Google Scholar 

  13. A. García D. andH. Salazar I.:J. Math. Phys. (N. Y.) 24, 2498 (1983).

    Article  ADS  Google Scholar 

  14. A. García D. Electrovac type-D solutions with cosmological constant, inJ. Math. Phys. (N. Y.), to appear.

  15. R. Debever andR. G. McLenaghan:J. Math. Phys. (N. Y.),8, 1711 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  16. J. F. Plebański andM. Demiański:Ann. Phys. (N. Y.),98, 98 (1976).

    Article  ADS  MATH  Google Scholar 

  17. W. Kinnersley andM. Walker:Phys. Rev. D,2, 1359 (1970).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. J. F. Plebański: report at theWartburg International Relativity Meeting, Wartburg, 1972.

  19. A. García D. andH. Salazar I.:Gen. Rel. Grav.,15, 417 (1983).

    Article  Google Scholar 

  20. J. F. Plebański:Ann. Phys. (N. Y.),90, 196 (1975).

    Article  ADS  MATH  Google Scholar 

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Author notes

  1. A. García D.

    Present address: Sección de Graduados, Escuela Superior de Ingeniería Mecánica y Eléctrica del LPN, Mexico, Mexico

  2. J. F. Plebański

    Present address: University of Warsaw, Warsaw, Poland

Authors and Affiliations

  1. Departmento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 0700, México, D.F.

    A. García D., H. Salazar I. & J. F. Plebański

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  1. A. García D.
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  2. H. Salazar I.
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  3. J. F. Plebański
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García D., A., Salazar I., H. & Plebański, J.F. Type-D solutions of the Einstein and Born-Infeld nonlinear-electrodynamics equations. Nuov Cim B 84, 65–90 (1984). https://doi.org/10.1007/BF02721649

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  • DOI: https://doi.org/10.1007/BF02721649