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Abstract
We calculate the perihelion precession of a test particle in the Edditington-Robertson parameterized metric via the rate of change of the Runge-Lenz vector. It is shown that the calculation results are the same as in the standard, isotropic and harmonic coordinates. These results provide concrete illustrations of the covariances of general relativity. In addition, we find some typos in the derivation of the perihelion precession via the Runge-Lenz vector in Weinberg's classic general relativity textbook, and this finding might also be useful for the beginners who are reading the textbook.
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