About the coordinate time for photons in Lifshitz space-times

  • J. R. VillanuevaEmail author
  • Yerko Vásquez
Regular Article - Theoretical Physics


In this paper we studied the behavior of radial photons from the point of view of the coordinate time in (asymptotically) Lifshitz space-times, and we found a generalization to the result reported in previous works by Cruz et al. (Eur. Phys. J. C 73:7, 2013), Olivares et al. (Astrophys. Space Sci. 347:83–89, 2013), and Olivares et al. (arXiv:1306.5285). We demonstrate that all asymptotically Lifshitz space-times characterized by a lapse function f(r) which tends to one when r→∞, present the same behavior, in the sense that an external observer will see that photons arrive at spatial infinity in a finite coordinate time. Also, we show that radial photons in the proper system cannot determine the presence of the black hole in the region r +<r<∞, because the proper time as a result is independent of the lapse function f(r).


Black Hole Event Horizon Proper Time Coordinate Time Massless Particle 
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YV is supported by FONDECYT grant 11121148; JRV thanks the UFRO for their hospitality and dedicates this work to JGDVB on his 10th birthday.


  1. 1.
    S. Kachru, X. Liu, M. Mulligan, Gravity duals of Lifshitz-like fixed points. Phys. Rev. D 78, 106005 (2008). arXiv:0808.1725 MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    S.A. Hartnoll, J. Polchinski, E. Silverstein, D. Tong, Towards strange metallic holography. J. High Energy Phys. 1004, 120 (2010) ADSCrossRefGoogle Scholar
  3. 3.
    K. Balasubramanian, J. McGreevy, An analytic Lifshitz black hole. Phys. Rev. D 80, 104039 (2009). arXiv:0909.0263 MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    M. Taylor, Non-relativistic holography. arXiv:0812.0530
  5. 5.
    R.B. Mann, Lifshitz topological black holes. J. High Energy Phys. 06, 075 (2009). arXiv:0905.1136 ADSCrossRefGoogle Scholar
  6. 6.
    G. Bertoldi, B.A. Burrington, A. Peet, Black Holes in asymptotically Lifshitz space-times with arbitrary critical exponent. Phys. Rev. D 80, 126003 (2009). arXiv:0905.3183 MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    E. Ayon-Beato, A. Garbarz, G. Giribet, M. Hassaine, Lifshitz black hole in three dimensions. Phys. Rev. D 80, 104029 (2009). arXiv:0909.1347 MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    M.H. Dehghani, R.B. Mann, Lovelock-Lifshitz black holes. J. High Energy Phys. 1007, 019 (2010). arXiv:1004.4397 MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    N. Cruz, M. Olivares, J.R. Villanueva, Geodesic structure of the Lifshitz black hole in 2+1 dimensions. Eur. Phys. J. C 73, 7 (2013). arXiv:1305.2133 Google Scholar
  10. 10.
    M. Olivares, G. Rojas, Y. Vásquez, J.R. Villanueva, Particles motion on topological Lifshitz black holes in 3+1 dimensions. Astrophys. Space Sci. 347, 83–89 (2013). arXiv:1304.4297 ADSCrossRefGoogle Scholar
  11. 11.
    M. Olivares, Y. Vásquez, J.R. Villanueva, F. Moncada, Motion of particles on a z=2 Lifshitz black hole in 3+1 dimensions (2013). arXiv:1306.5285
  12. 12.
    N. Cruz, M. Olivares, J.R. Villanueva, The geodesic structure of the Schwarzschild anti-de sitter black hole. Class. Quantum Gravity 22, 1167–1190 (2005). arXiv:gr-qc/0408016 MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. 13.
    E. Ayon-Beato, A. Garbarz, G. Giribet, M. Hassaine, Analytic Lifshitz black holes in higher dimensions. J. High Energy Phys. 1004, 030 (2010). arXiv:1001.2361 MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Departamento de Física y Astronomía, Facultad de CienciasUniversidad de ValparaísoValparaísoChile
  2. 2.Centro de Astrofísica de ValparaísoValparaísoChile
  3. 3.Departamento de Ciencias Físicas, Facultad de Ingeniería, Ciencias y AdministraciónUniversidad de La FronteraTemucoChile
  4. 4.Departamento de Físicas, Facultad de CienciasUniversidad de La SerenaLa SerenaChile

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