Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 3(4), pp. 45 - 49
DOI: 10.13189/ujcmj.2015.030401
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Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method

V. K. Shchigolev ^*
Department of Theoretical Physics, Ulyanovsk State University, 42 L. Tolstoy Str., Ulyanovsk 432000, Russia

ABSTRACT

We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to compare the HPM solution for orbits with those obtained earlier. Moreover, we obtain an approximate HPM solution for the Reissner-Nordstorm spacetime of a charged star.

KEYWORDS
Planetary Orbits, General Relativity, Perihelion Precession, Homotopy Perturbation Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] V. K. Shchigolev , "Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 3, No. 4, pp. 45 - 49, 2015. DOI: 10.13189/ujcmj.2015.030401.

(b). APA Format:
V. K. Shchigolev (2015). Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 3(4), 45 - 49. DOI: 10.13189/ujcmj.2015.030401.