Ibrar Hussain, Fazal M. Mahomed, Asghar Qadir, “Second-Order Approximate Symmetries of the Geodesic Equations for the Reissner–Nordström Metric and Re-Scaling of Energy of a Test Particle”, SIGMA, 2007, Volume 3,115, 9 pp.

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Second-Order Approximate Symmetries of the Geodesic Equations for the Reissner–Nordström Metric and Re-Scaling of Energy of a Test Particle

Ibrar Hussain^ab, Fazal M. Mahomed^c, Asghar Qadir^ab

^a Centre for Advanced Math. and Phys., National University of Sciences and Technology
^b Campus of the College of Electr. and Mech. Eng., Peshawar Road, Rawalpindi, Pakistan
^c School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Afric

Abstract: Following the use of approximate symmetries for the Schwarzschild spacetime by A. H. Kara, F. M. Mahomed and A. Qadir (Nonlinear Dynam., to appear), we have investigated the exact and approximate symmetries of the system of geodesic equations for the Reissner–Nordström spacetime (RN). For this purpose we are forced to use second order approximate symmetries. It is shown that in the second-order approximation, energy must be rescaled for the RN metric. The implications of this rescaling are discussed.

Keywords: Reissner–Nordström metric; geodesic equations; second-order approximate symmetries.

MSC: 83C40; 70S10

Received: August 14, 2007; in final form November 16, 2007; Published online December 7, 2007

Language: English

DOI: 10.3842/SIGMA.2007.115