Isaac Scientific Publishing

New Horizons in Mathematical Physics

Field Approach for General Relativity

Download PDF (210.3 KB) PP. 31 - 40 Pub. Date: June 30, 2021

DOI: 10.22606/nhmp.2021.52001


  • Ali Rıza ŞAHİN*
    Milli Eğitim Bakanlığı, İstanbul Atatürk Anadolu Lisesi, İstanbul, Turkey


The general theory of relativity is based on expressing gravity by means of the metric tensor and its elements instead of some fields as in electrodynamics. This work starts with by defining some vector fields for metric or metric tensor. After metric and metric tensor are expressed in terms of these fields, the geodesic equations and Einstein equations are derived for these fields. Finally, perihelion precession and light deflection are recalculated, as two different applications of the introduced fields.


metric tensor, geodesic equations, Lorentz force, Einstein equations, Maxwell equations Schwarzschild metric, perihelion precession, light deflection.


[1] S.M. Wagh, “Some fundamental issues in General Relativity and their resolution”, Available:

[2] C. W. Misner, K. P. Thorne and J. A. Wheeler, Gravitation. Freeman and Company, 1973, pp. 216-218.

[3] Covariant Formulation of Electrodynamics, Available: phy319/node135.html

[4] J. D. Jackson, Classical Electrodynamics. John Wiley & Sons, 1999, pp. 608-610.

[5] Schwarzschild radius, Available:

[6] Schwarzschild metric, Available:

[7] L Clemence, G. M. "The Relativity Effect in Planetary Motions". Reviews of Modern Physics, vol. 19 (4), pp. 361– 364

[8] C. Magnan, “Complete calculations of the perihelion precession of Mercury and the deflection of light by the Sun in General Relativity”, Available:

[9] G. Hooft, Introduction to General Relativity. Utrecht University, 1998, pp. 53-54. Available: https://webspace.

[10] Texas Mauritanian Eclipse Team, “Gravitational deflection of light: solar eclipse of 30 June 1973 I. Description of procedures and final result”. Astronomical Journal, vol. 81, pp. 452-454. Available: http://articles.adsabs.

[11] H. C, Ohanian and R. Ruffuni, Gravitation and Spacetime. Cambridge University, 2013, pp. 138-142.

[12] E. Fomalont, S. Kopeikin, G. Lanyi, J. Benson, “Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA”, The Astrophysical Journal, Volume 699, Number 2, pp. 1395-1402. Available: