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The metric perturbation induced by a particle in the Schwarzschild backgroundis usually calculated in the Regge-Wheeler (RW) gauge, whereas thegravitational self-force is known to be given by the tail part of the metricperturbation in the harmonic gauge. Thus, to identify the gravitationalself-force correctly in a specified gauge, it is necessary to find out a gaugetransformation that connects these two gauges. This is called the gaugeproblem. As a direct approach to solve the gauge problem, we formulate a methodto calculate the metric perturbation in the harmonic gauge on the Schwarzshildbackgound. We apply the Fourier-harmonic expansion to the metric perturbationand reduce the problem to the gauge transformation of the Fourier-harmoniccoefficients (radial functions) from the RW gauge to the harmonic gauge. Wederive a set of decoupled radial equations for the gauge transformation. Theseequations are found to have a simple second-order form for the odd parity partand the forms of spin $s=0$ and 1 Teukolsky equations for the even parity part.As a by-product, we correct typos in Zerilli's paper and present a set ofcorrected equations in Appendix.Comment: Revtex4, 13 pages, no figure

Gauge problem in the gravitational self-force: Harmonic gauge approach in the Schwarzschild background