Comment on “The equivalence principle in the Schwarzschild geometry” [Am. J. Phys. 62, 1037 (1994)]

In the article “The equivalence principle in the Schwarzschild geometry” [Am. J. Phys. 62, 1037–1040 (1994)], some manifestation of the equivalence principle in Schwarzschild spacetime was studied. We point out that the result for the Riemann-tensor component in this article is incorrect because only the first order terms in the metric expansion are taken into account. We show the corrected result, illustrating the importance of the second order terms in the approximate metric in computing curvature quantities.