Abstract
We derive the five dimensional Myers–Perry metric via an elementary method to solve the vacuum Einstein field equations directly. This method firstly proposed by Clotz is very simple since it merely involves four components of Ricci tensor and only requires us to deal with some equations without second derivatives’ terms when the metric ansatz is assumed to take an appropriate form.
Similar content being viewed by others
References
Myers R.C. and Perry M.J. (1986). Ann. Phys. (N.Y.) 172: 304
Emparan, R., Reall, H.S.: Phys. Rev. Lett. 88, 101101, hep-th/0110260 (2002)
Elvang, H., Emparan, R., Mateos, D., Reall, H.S.: Phys. Rev. Lett. 93, 211302, hep-th/0407065 (2004)
Emparan, R., Reall, H.S.: arXiv:0801.3471 [hep-th]
Harmark T. (2004). Phys. Rev. D 70: 124002
Harmark T. and Olesen P. (2005). Phys. Rev. D 72: 124017
Aliev, A.N.: Mod. Phys. Lett. A 21, 751 gr-qc/0505003 (2006)
Shuang-Qing Wu.: Phys. Rev. Lett. 100, 121301, arXiv:0709.1749 [hep-th] (2008)
Dimopoulos S. and Landsberg G. (2001). Phys. Rev. Lett. 87: 161602
Giddings S.B. and Thomas S.D. (2002). Phys. Rev. D 65: 056010
Kanti, P.: Int. J. Mod. Phys. A 19, 4899 hep-ph/0402168 (2004)
Ernst F.J. (1968). Phys. Rev. 167: 1175
Ernst F.J. (1968). Phys. Rev. 168: 1415
Stephani H., Kramer D., MacCallum M., Hoenselaers C. and Herlt E. (2003). Exact Solutions of Einsteins Field Equations, 2nd edn. Cambridge University Press, Cambridge
Kerr R.P. (1963). Phys. Rev. Lett. 11: 237
Newman E.T., Couch E., Chinapared K., Exton A., Prakash A. and Torrence R. (1965). J. Math. Phys. 6: 918
Pomeransky, A.A., Sen’kov, R.A.: hep-th/0612005
Lü, H., Mei, J.W., Pope, C.N.: arXiv:0804.1152 [hep-th]
Pomeransky, A.A.: Phys. Rev. D 73, 044004, hep-th/0507250 (2006)
Giusto, S., Saxena, A.: Class. Quantum Grav. 24, 4269, arXiv:0705.4484 [hep-th] (2007)
Clotz A.H. (1982). Gen. Rel. Grav. 14: 727
Gui Y.X., Zhang J.G., Zhang Y. and Chen F.P. (1984). Acta Phys. Sin. 33: 1129
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Peng, JJ. An elementary derivation of the five dimensional Myers–Perry metric. Gen Relativ Gravit 41, 147–152 (2009). https://doi.org/10.1007/s10714-008-0660-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-008-0660-2