Abstract
The object of study is the geodesic structure of a \(z=2\) Lifshitz black hole in 3+1 space–time dimensions, which is an exact solution to the Einstein-scalar-Maxwell theory. The motion of massless and massive particles in this background is researched using the standard Lagrangian procedure. Analytical expressions are obtained for radial and angular motions of the test particles, where the polar trajectories are given in terms of the \(\wp \)-Weierstraß elliptic function. It will be demonstrated that an external observer can see that photons with radial motion arrive at spatial infinity in a finite coordinate time. For particles with non-vanished angular momentum, the motion is studied on the invariant plane \(\phi = \pi /2\) and, it is shown that bounded orbits are not allowed for this space–time on this plane. These results are consistent with other recent studies on Lifshitz black holes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amado, I., Faedo, A.F.: Lifshitz black holes in string theory. JHEP 1107, 004 (2011). arXiv: 1105.4862
Ayon-Beato, E., Garbarz, A., Giribet, G., Hassaine, M.: Lifshitz black hole in three dimensions. Phys. Rev. D 80, 104029 (2009)
Balasubramanian, K., McGreevy, J.: An analytic Lifshitz black hole. Phys. Rev. D 80, 104039 (2009)
Brynjolfsson, E.J., Danielsson, U.H., Thorlacius, L., Zingg, T.: Holographic superconductors with Lifshitz scaling. J. Phys. A 43, 065401 (2010). arXiv: 0908.2611
Cruz, N., Olivares, M., Villanueva, J.R.: Geodesic structure of Lifshitz black holes in 2+1 dimensions. Eur. Phys. J. C 73, 2485 (2013). arXiv: 1305.2133
Cruz, N., Olivares, M., Villanueva, J.R.: The geodesic structure of the Schwarzschild anti-de sitter black hole. Class. Quantum Grav. 22, 1167–1190 (2005). arXiv: 0408016
Dehghani, M.H., Mann, R.B.: Lovelock-Lifshitz black holes. JHEP 1007, 019 (2010)
Devecioglu, D.O., Sarioglu, O.: On the thermodynamics of Lifshitz black holes. Phys. Rev. D 83, 124041 (2011). arXiv: 1103.1993
Hartnoll, S.A., Polchinski, J., Silverstein, E., Tong, D.: Towards strange metallic holography. JHEP 1004, 120 (2010)
Kachru, S., Liu, X., Mulligan, M.: Gravity duals of Lifshitz-like fixed points. Phys. Rev. D 78, 106005 (2008)
Maeda, H., Giribet, G.: Lifshitz black holes in Brans-Dicke theory. JHEP 1111, 015 (2011). [ arXiv: 1105.1331]
Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)
Mann, R.B.: Lifshitz topological black holes. JHEP 06, 075 (2009)
Myung, Y.S., Moon, T.: Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes. Phys. Rev. D 86, 024006 (2012). arXiv: 1204.2116
Myung, Y.S.: Phase transitions for the Lifshitz black holes. Eur. Phys. J. C 72, 2116 (2012). arXiv: 1203.1367
Olivares, M., Rojas, G., Vásquez, Y., Villanueva, J.R.: Particles motion on topological Lifshitz black holes in 3+1 dimensions. Astrophys. Space Sci. 347, 83–89 (2013). arXiv: 1304.4297
Olivares, M., Villanueva, J.R.: Massive neutral particles on heterotic string theory. Eur. Phys. J. C 73, 2659 (2013). arXiv: 1311.4236
Pang, D.W.: Conductivity and diffusion constant in Lifshitz backgrounds. JHEP 1001, 120 (2010)
Taylor, M.: Non-relativistic holography (2008). arXiv:0812.0530
Villanueva, J.R., Olivares, M.: On the null trajectories in conformal Weyl Gravity. J. Cosmol. Astropart. Phys. 1306, 040 (2013). arXiv: 1305.3922
Villanueva, J.R., Vásquez, Y.: About the coordinate time in Lifshitz space–times. Eur. Phys. J. C 73, 2587 (2013). arXiv: 1309.4417
Acknowledgments
The authors would like to thank F. Ercolí, M. Curé and referees for their comments and suggestions that helped us improve this paper. This work was funded by the Comisión Nacional de Investigación Científica y Tecnológica through FONDECYT Grants 11121148 (YV, FM) and 11130695 (JRV), and also partially funded by the Dirección de Investigación, Universidad de La Frontera (FM). MO would also like to thank PUCV and Instituto de Física y Astronomía (UV) and JRV wishes to thank to the UFRO for their hospitality.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Olivares, M., Vásquez, Y., Villanueva, J.R. et al. Motion of particles on a \(z=2\) Lifshitz black hole background in 3\(+\)1 dimensions. Celest Mech Dyn Astr 119, 207–217 (2014). https://doi.org/10.1007/s10569-014-9555-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10569-014-9555-6