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We provide a prescription to solve the metric completion problem ingravitational self-force calculations on a Kerr spacetime by fixing theremaining gauge freedom. We discuss the explicit example of eccentricequatorial orbits, recovering all limiting cases already studied in theliterature of eccentric orbits in Schwarzschild as well as circular orbits inboth Schwarzschild and Kerr spacetimes.

Gauge-fixing for the completion problem of reconstructed metric perturbations of a Kerr spacetime