Skip to main content
SpringerLink
Log in

Boost-rotation symmetric spacetimes – Review

  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

Boost-rotation symmetric spacetimes are the only locally asymptotically flat axially symmetric electrovacuum spacetimes with a further symmetry that are radiative. They are realized by uniformly accelerated particles of various kinds or black holes. Their general properties are summarized. Several examples of boost-rotation symmetric solutions of the Maxwell and Einstein equations are studied: uniformly accelerated electric and magnetic multipoles, the Bonnor-Swaminarayan solutions, the C-metric and the spinning C-metric.

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

Similar content being viewed by others

References

  1. A. Ashtekar and B.G. Schmidt: J. Math. Phys. 21 (1980) 862.

    Google Scholar 

  2. J. Bičák: in Relativistic Gravitation and Gravitational Radiation, Proc. Les Houches School of Physics (Eds. J.-A. Marck and J.-P. Lasota), Cambridge University Press, Cambridge, 1995, p. 67.

    Google Scholar 

  3. J. Bičák: in Einstein's Field Equations and Their Physical Meaning (Ed. B.G. Schmidt), Springer Verlag, Berlin-New York, 2000.

    Google Scholar 

  4. J. Bičák: Exact radiative spacetimes, some recent developments, to appear in Ann. Phys. (Germany) (2000).

  5. J. Bičák and B.G. Schmidt: J. Math. Phys. 25 (1984) 600.

    Google Scholar 

  6. J. Bičák and A. Pravdová: J. Math. Phys. 39 (1998) 6011.

    Google Scholar 

  7. J. Bičák, P. Reilly, and J. Winicour: Gen. Rel. Grav. 20 (1988) 171.

    Google Scholar 

  8. R. Goméz, P. Papadopoulos, and J. Winicour: J. Math. Phys. 35 (1994) 4184.

    Google Scholar 

  9. M. Alcubierre, C. Grundlach, and F. Siebel: in Abstr. 15th Int. Conf. on Gen. Rel. Grav., Pune, 1997, p. 83.

  10. T. Levi-Civita: Rend. Acc. Lincei 27 (1918) 343.

    Google Scholar 

  11. H. Weyl: Ann. Phys. (Germany) [59] (1919) 185.

    Google Scholar 

  12. W.B. Bonnor and N.S. Swaminarayan: Z. Phys. 177 (1964) 240. See also W. Israel and K.A. Khan: Nuovo Cim. 33 (1964) 331.

    Google Scholar 

  13. J. Bičák, C. Hoenselaers, and B.G. Schmidt: Proc. Roy. Soc. (Lond.) A 390 (1983) 411.

    Google Scholar 

  14. W. Kinnersley and M. Walker: Phys. Rev. D 2 (1970) 1359.

    Google Scholar 

  15. J.F. Plebański and M. Demiański: Ann. Phys. (USA) 98 (1976) 98.

    Google Scholar 

  16. J. Bičák and V. Pravda: Phys. Rev. D 60 (1999) 044004.

    Google Scholar 

  17. F.J. Ernst: J. Math. Phys. 19 (1978) 1986.

    Google Scholar 

  18. F.J. Ernst: J. Math. Phys. 17 (1976) 515.

    Google Scholar 

  19. J. Bičák and B.G. Schmidt: Phys. Rev. D 40 (1989) 1827.

    Google Scholar 

  20. H. Bondi, M.G.J. van der Burg, and A.W.K. Metzner: Proc. Roy. Soc. (Lond.) A 269 (1962) 21.

    Google Scholar 

  21. R.K. Sachs: Proc. Roy. Soc. A 270 (1962) 103.

    Google Scholar 

  22. M.G.J. van der Burg: Proc. Roy. Soc. A 310 (1969) 221.

    Google Scholar 

  23. U. von der Gönna and D. Kramer: Class. Quantum Grav. 15 (1998) 215.

    Google Scholar 

  24. P.T. Chruściel, M.A.H. MacCallum, and D.B. Singleton: Philos. Trans. R. Soc. A 350 (1995) 113.

    Google Scholar 

  25. R. Wald: General Relativity, The University of Chicago Press, Chicago, 1984.

    Google Scholar 

  26. A. Ashtekar, J. Bičák, and B.G. Schmidt: Phys. Rev. D 55 (1997) 669.

    Google Scholar 

  27. M.G.J. van der Burg: Proc. Roy. Soc. (Lond.) A 294 (1966) 112.

    Google Scholar 

  28. A. Pravdová: Symmetries of asymptotically flat spacetimes and radiation, Ph.D. Thesis, Department of Theoretical Physics, Charles University, Prague, 1999.

    Google Scholar 

  29. J. Bičák and A. Pravdová: Class. Quantum Grav. 16 (1999) 2023.

    Google Scholar 

  30. J.A. Valiente Kroon: On Killing vector fiels and Newman-Penrose constants, J. Math. Phys. [41] (2000) 898; see also gr-qc/9903093 (1999).

    Google Scholar 

  31. J. Bičák: in Conference on Math. Relativity (Ed. R. Bartnik), Proc. of the Centre for Mathem. Analysis, Vol. 19, Australian Nat. Univ., Canberra, 1989.

    Google Scholar 

  32. J. Bičák: in Galaxies, axisymmetric systems and relativity (Ed. M.A.H. MacCallum), Cambridge University Press, Cambridge, 1985.

    Google Scholar 

  33. A. Einstein and N.J. Rosen: J. Franklin Inst. 223 (1937) 43.

    Google Scholar 

  34. D. Kramer, H. Stephani, E. Herlt, and M. MacCallum: Exact solutions of Einstein's field equations, Cambridge University Press, Cambridge, 1980.

    Google Scholar 

  35. H. Friedrich: Commun. Math. Phys. 107 (1986) 587.

    Google Scholar 

  36. C. Cutler and R.M. Wald: Class. Quantum Grav. 6 (1989) 453.

    Google Scholar 

  37. D. Christodoulou and S. Klainerman: The non linear stability of the Minkowski space-time, Princeton University Press, Princeton, 1994.

    Google Scholar 

  38. J. Bičák, C. Hoenselaers, and B.G. Schmidt: Proc. Roy. Soc. (Lond.) A 390 (1983) 397.

    Google Scholar 

  39. S.W. Hawking, G.T. Horowitz, and S.F. Ross: Phys. Rev. D 51 1995) 4302.

    Google Scholar 

  40. J. Bičák: Proc. Roy. Soc. (Lond.) A 371 (1980) 429.

    Google Scholar 

  41. M. Born: Ann. Phys. (Germany) 30 (1909) 1.

    Google Scholar 

  42. F. Rohrlich: Classical charged particles, Addison-Wesley, Reading, Mass., 1965.

    Google Scholar 

  43. J. Bičák: Proc. Roy. Soc. (Lond.) A 302 (1968) 201.

    Google Scholar 

  44. J. Bičák and R. Muschall: Electromagnetic fields and radiation patterns from multipoles in hyperbolic motion, Wiss. Z. Univ. Jena 39 (1990) 15.

    Google Scholar 

  45. V. Pravda: Exact radiative spacetimes: selected problems, Ph.D. Thesis, Department of Theoretical Physics, Charles University, Prague, 1999.

    Google Scholar 

  46. V. Pravda and A. Pravdová: in Proc. of the Week of Postgraduate Students, Faculty of mathematics and physics, Charles university, Prague, 1998, p. 377; gr-qc/9806114 (1998).

    Google Scholar 

  47. W. Pauli: Relativitätstheorie, Leipzig, Teubner, 1918.

    Google Scholar 

  48. M. Laue: Relativitätstheorie, Braunschweig, Vieweg, 1919.

    Google Scholar 

  49. A.K. Singal: Gen. Rel. Grav. 29 (1997) 1371.

    Google Scholar 

  50. S. Parrot: Gen. Rel. Grav. 29 (1997) 1463.

    Google Scholar 

  51. A. Harpaz and N. Soker: Gen. Rel. Grav. 30 (1998) 1217.

    Google Scholar 

  52. H. Bondi: Rev. Mod. Phys. 29 (1957) 423.

    Google Scholar 

  53. J. Bičák: in Gravitation and Geometry (Eds. W. Rindler and A. Trautman), Bibliopolis, Naples, 1987.

    Google Scholar 

  54. J. Bičák and B.G. Schmidt: Class. Quantum Grav. 6 (1989) 1547.

    Google Scholar 

  55. J. Ehlers and W. Kundt: in Gravitation: an introduction to current research (Ed. L. Witten), Wiley, New York, London, 1962.

    Google Scholar 

  56. I. Robinson and A. Trautman: Proc. Roy. Soc. (Lond.) A 265 (1962) 463.

    Google Scholar 

  57. W. Kinnersley and M. Walker: Phys. Rev. D 2 (1970) 1359.

    Google Scholar 

  58. A. Ashtekar and T. Dray: Comm. Phys. 79 (1981) 581. T. Dray: Gen. Rel. Grav. 14 (1982) 109. T. Dray: The asymptotic structure of a family of Einstein-Maxwell solutions, Ph.D. Thesis, University of California, Berkeley, 1981.

    Google Scholar 

  59. H. Farhoosh and R.L. Zimmerman: J. Math. Phys. 20 (1979) 2272. H. Farhoosh and R.L. Zimmerman: Phys. Rev. D 21 (1980) 317. H. Farhoosh and R.L. Zimmerman: Phys. Rev. D 21 (1980) 2064. R.L. Zimmerman and H. Farhoosh: Gen. Rel. Grav. 12 (1980) 935. H. Farhoosh and R.L. Zimmerman: Phys. Rev. D 23 (1981) 299.

    Google Scholar 

  60. W.B. Bonnor: Gen. Rel. Grav. 15 (1983) 535.

    Google Scholar 

  61. W.B. Bonnor: Gen. Rel. Grav. 16 (1984) 269.

    Google Scholar 

  62. F.H.J. Cornish and W.J. Uttley: Gen. Rel. Grav. 27 (1995) 439; 735.

    Google Scholar 

  63. W. Yongcheng: Phys. Rev. D 55 (1997) 7977.

    Google Scholar 

  64. C.G. Wells: gr-qc/9808044 (1998).

  65. P.S. Letelier and S.R. Oliveira: gr-qc/9809089 (1998).

  66. J. Bičák: C-metric, unpublished.

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Acad. Sci. CR, Žitná 25, 115 67, Prague 1, Czech Republic

    V. Pravda

  2. Mathematical Institute, Acad. Sci. CR, Žitná 25, 115 67, Prague 1, Czech Republic

    A. Pravdová

Authors
  1. V. Pravda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Pravdová
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pravda, V., Pravdová, A. Boost-rotation symmetric spacetimes – Review. Czechoslovak Journal of Physics 50, 333–375 (2000). https://doi.org/10.1023/A:1022862309863

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022862309863

Keywords

Search

Navigation