Radiative Spacetimes

  • Bičàk J. 
Conference paper


The question of existence of general, asymptotically flat radiative spacetimes and examples of explicit classes of radiative solutions of Einstein’s field equations are discussed in the light of some new developments. The examples are cylindrical waves, Robinson-Trautman and type N spacetimes, and especially boost- rotation symmetric spacetimes, representing uniformly accelerated particles or black holes.


Black Hole Gravitational Wave Killing Vector Gravitational Radiation Cauchy Hypersurface 
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  1. 1.
    Bondi, H., van der Burg, M.G.J., Metzner, A.W.K. (1962): Gravitational waves in general relativity. VIL Waves from Axi-symmetric isolated systems. Proc. Roy. Soc. Lond. A 269, 21ADSMATHCrossRefGoogle Scholar
  2. 2.
    Sachs, R.K. (1962): Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time. Proc. Roy. Soc. Lond. A 270, 103MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Newman, E.T., Penrose, R. (1962): An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. 3, 566MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Penrose, R. (1963): Asymptotic properties of fields and space-times. Phys. Rev. Lett. 10, 66MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Christodoulou, D., Klainerman, S. (1994): The nonlinear stability of the Minkowski spacetime. Princeton University Press, PrincetonGoogle Scholar
  6. 6.
    Chruściel, P., MacCallum, M.A.H., Singleton, P.B. (1995): Gravitational waves in general relativity XIV. Bondi expansions and the “polyhomogeneity” of J. Phil. Trans. Roy. Soc. Lond. A350, 113ADSGoogle Scholar
  7. 7.
    Friedrich, H. (1998): Einstein’s equation and geometric asymptotics, in Gravitation and relativity: At the turn of the millenium, ed. by N. Dadhich, J. Narlikar, Proceedings of the GR-15 conference, Inter-University Centre for Astronomy and Astrophysics Press, PuneGoogle Scholar
  8. 8.
    Friedrich, H. (1986): On the existence of n-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure. Commun. Math. Phys. 107, 587MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Friedrich, H. (1995): Einstein equations and conformai structure: Existence of anti-de Sitter-type space-times. J. Geom. Phys. 17, 125MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    Bičák, J. (2000): Selected solutions of Einstein’s field equations: their role in general relativity and astrophysics, in Einstein’s Field Equations and Their Physical Meaning, ed. by B.G. Schmidt, Springer Verlag Berlin Heidelberg New YorkGoogle Scholar
  11. 11.
    Bičák, J. (2000): Exact ratiative Spacetimes: Some recent developments. Annalen Phys. 9, 207–216ADSMATHCrossRefGoogle Scholar
  12. 12.
    Ashtekar, A., Bičák, J., Schmidt, B.G. (1997): Asymptotic structure of symmetry-reduced general relativity. Phys. Rev. D 55, 669MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Ashtekar, A., Bičák, J., Schmidt, B.G. (1997): Behaviour of Einstein-Rosen waves at null infinity. Phys. Rev. D 55, 687MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Chruściel, P.T. (1992): On the global structure of Robinson-Trautman space-times. Proc. Roy. Soc. Lond. A 436, 299; Chruściel, P.T., Singleton, D.B. (1992): Non-smoothness of event horizons of Robinson-Trautman black holes. Commun. Math. Phys. 147, 137ADSMATHCrossRefGoogle Scholar
  15. 15.
    Bičák, J., Podolský, J. (1997): The global structure of Robinson-Trautman radiative spacetimes with cosmological constant. Phys. Rev. D 55, 1985MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Bičák, J., Podolský, J. (1995): Cosmic no-hair conjecture and black-hole formation: An exact model with gravitational radiation. Phys. Rev. D 52, 887MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Stephani, H. (1993): A note on the solutions of the diverging twisting, type N, vacuum field equations. Class. Quantum Grav. 10, 2187MathSciNetADSMATHCrossRefGoogle Scholar
  18. 18.
    Finley, J.D., Plebański, J.F., Przanowski, M. (1997): An iterative approach to twisting and diverging, type N vacuum Einstein equations: A (third order) resolution of Stephani’s paradox. Class. Quant. Grav. 14, 489ADSMATHCrossRefGoogle Scholar
  19. 19.
    Bičák, J., Pravda, V. (1998): Curvature invariants in type N spacetimes. Class. Quantum Grav. 15, 1539ADSMATHCrossRefGoogle Scholar
  20. 20.
    MacAlevey, P. (1999): Approximate solutions of Einstein’s vacuum field equations in the type N, twisting and diverging case. Class. Quantum Grav. 16, 2259MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    Mason, L. (1998): The asymptotic structure of algebraically special spacetimes. Class. Quantum Grav. 15, 1019ADSMATHCrossRefGoogle Scholar
  22. 22.
    Bičák, J. (1997): Radiative spacetimes: Exact approaches, in Relativistic Gravitation and Gravitational Radiation Proceedings of the Les Houches School of Physics, ed. by J.-A. Marck, J.-P. Lasota, Cambridge University Press, CambridgeGoogle Scholar
  23. 23.
    Bičák, J., Pravdová, A. (1998): Symmetries of asymptotically flat electrovacuum spacetimes and radiation. J. Math. Phys. 39, 6011MathSciNetADSMATHCrossRefGoogle Scholar
  24. 24.
    Bičák, J., Pravdová, A. (1999): Axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity. Class. Quantum Grav. 16, 2023ADSMATHCrossRefGoogle Scholar
  25. 25.
    Valiente-Kroon, J.A. (2000): On Killing vector fields and Newman-Penrose constants. J. Math. Phys. 41, 898MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Bičák, J., Schmidt, B.G. (1989): Asymptotically flat radiative space-times with boostrotation symmetry: The general structure. Phys. Rev. D 40, 1827MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    Pravda, V., Pravdová, A. (2000): Boost-rotation symmetric spacetimes — review. Czech. J. Physics 50, 333ADSCrossRefGoogle Scholar
  28. 28.
    Kramer, D., Stephani, H., Herlt, E., MacCallum, M.A.H. (1980): Exact solutions of Einstein’s field equations. Cambridge University Press, CambridgeMATHGoogle Scholar
  29. 29.
    Plebański, J., Demiański, M. (1976): Rotating, charged and uniformly accelerating mass in general relativity. Ann. Phys. (N.Y.) 98, 98ADSMATHCrossRefGoogle Scholar
  30. 30.
    Bičák, J., Pravda, V. (1999): Spinning C-metric: Radiative spacetime with accelerating, rotating black holes. Phys. Rev. D 60, 044004MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsCharles UniversityPragueCzech Republic

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