We provide a prescription to solve the metric completion problem in gravitational self-force calculations on a Kerr spacetime by fixing the remaining gauge freedom. We discuss the explicit example of eccentric equatorial orbits, recovering all limiting cases already studied in the literature of eccentric orbits in Schwarzschild as well as circular orbits in both Schwarzschild and Kerr spacetimes.
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Bini et al. (2019) studied this question.
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