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Journal of High Energy Physics

, 2010:101 | Cite as

5D gravitational waves from complexified black rings

  • N. Bretón
  • A. Feinstein
  • L. A. López
Article

Abstract

In this paper we construct and briefly study the 5D time-dependent solutions of general relativity obtained via double analytic continuation of the black hole (Myers-Perry) and of the black ring solutions with a double (Pomeransky-Senkov) and a single rotation (Emparan-Reall). The new solutions take the form of a generalized Einstein-Rosen cosmology representing gravitational waves propagating in a closed universe. In this context the rotation parameters of the rings can be interpreted as the extra wave polarizations, while it is interesting to state that the waves obtained from Myers-Perry Black holes exhibit an extra boost-rotational symmetry in higher dimensions which signals their better behavior at null infinity. The analogue to the C-energy is analyzed.

Keywords

Classical Theories of Gravity Black Holes 

References

  1. [1]
    O. Aharony, M. Fabinger, G.T. Horowitz and E. Silverstein, Clean time-dependent string backgrounds from bubble baths, JHEP 07 (2002) 007 [hep-th/0204158] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [SPIRES].CrossRefADSGoogle Scholar
  3. [3]
    F. Dowker, J.P. Gauntlett, G.W. Gibbons and G.T. Horowitz, Nucleation of P-Branes and Fundamental Strings, Phys. Rev. D 53 (1996) 7115 [hep-th/9512154] [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    G.T. Horowitz and R.C. Myers, AdS-CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1999) 026005 [hep-th/9808079] [SPIRES].MathSciNetADSGoogle Scholar
  5. [5]
    D. Ida, T. Shiromizu and H. Ochiai, Semiclassical instability of the brane-world: Randall-Sundrum bubbles, Phys. Rev. D 65 (2002) 023504 [hep-th/0108056] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    M.S. Costa and M. Gutperle, The Kaluza-Klein Melvin solution in M-theory, JHEP 03 (2001) 027 [hep-th/0012072] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    M. Fabinger and P. Hořava, Casimir effect between world-branes in heterotic M-theory, Nucl. Phys. B 580 (2000) 243 [hep-th/0002073] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    T. Piran, P.N. Safier and J. Katz, Cylindrical gravitational waves with two degrees of freedom: an exact solution, Phys. Rev. D 34 (1986) 331 [SPIRES].ADSGoogle Scholar
  9. [9]
    T. Piran, P.N. Safier and R.F. Stark, A general numerical solution of cylindrical gravitational waves, Phys. Rev. D 32 (1985) 3101 [SPIRES].ADSGoogle Scholar
  10. [10]
    M. Carmeli, C. Charach and S. Malin, Survey of cosmological models with gravitational, scalar and electromagnetic waves, Phys. Rept. 76 (1981) 79 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  11. [11]
    M. Carmeli and Ch. Charach, The Einstein-Rosen Gravitational waves and cosmology, Found. of Physics 14 (1984) 963.CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    A. Feinstein and J. Ibáñez, Curvature-singularity-free solutions for colliding plane gravitational waves with broken u-v symmetry, Phys. Rev. D 39 (1989) 470 [SPIRES].ADSGoogle Scholar
  13. [13]
    R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Ann. Phys. 172 (1986) 304 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  14. [14]
    T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [SPIRES].MathSciNetADSGoogle Scholar
  15. [15]
    T. Harmark and P. Olesen, On the structure of stationary and axisymmetric metrics, Phys. Rev. D 72 (2005) 124017 [hep-th/0508208] [SPIRES].MathSciNetADSGoogle Scholar
  16. [16]
    J.M.M. Senovilla, Trapped surfaces, horizons and exact solutions in higher dimensions, Class. Quant. Grav. 19 (2002) L113 [hep-th/0204005] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    C.W. Misner, The flatter regions of Newman, Unti, and Tamburino’s generalized Schwarzschild space, J. Math. Phys. 4 (1963) 924.CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    S.M. C.V. Goncalves, Unpolarized radiative cylindrical spacetimes: Trapped surfaces and quasilocal energy, Class. Quant. Grav. 20 (2003) 37 [gr-qc/0212125] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  19. [19]
    J. Bičak and B. Schmidt, Asymptotically flat radiative space-times with boost-rotation symmetry: The general structure, Phys. Rev. D 40 (1989) 1827.ADSGoogle Scholar
  20. [20]
    R.H. Gowdy and B.D. Edmonds, Cylindrical gravitational waves in expanding universes: Models for waves from compact sources, Phys. Rev. D 75 (2007) 084011 [gr-qc/0701161] [SPIRES].MathSciNetADSGoogle Scholar
  21. [21]
    A.A. Pomeransky and R.A. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [SPIRES].
  22. [22]
    H. Elvang and M.J. Rodriguez, Bicycling Black Rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    R. Emparan and H.S. Reall, A rotating black ring in five dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [SPIRES].MathSciNetADSGoogle Scholar
  25. [25]
    G.A. Korn and T.M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1968), Chap. 21.Google Scholar
  26. [26]
    I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, N.Y. U.S.A. (1980).MATHGoogle Scholar
  27. [27]
    M. Carmeli, C. Charach and A. Feinstein, Inhomogeneous mixmaster universes: some exact solutions, Ann. Phys. 150 (1983) 392 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  28. [28]
    R. Gowdy, Gravitational waves in closed universes, Phys. Rev. Lett. 27 (1971) 826.CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Dpto. de Física, Centro de Investigación y de Estudios Avanzados del I. P. N.D.F.México
  2. 2.Dpto. de Física TeóricaUniversidad del PaísBilbaoSpain

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