  The gravitational waves emitted by binary systems with extreme-mass ratios
carry unique astrophysical information that can only be detected by space-based
detectors like eLISA. To that end, a very accurate modelling of the system is
required. The gravitational self-force program, which has been fully developed
in the Lorenz gauge, is the best approach we have so far. However, the
computations required would be done more efficiently if we could work in other
gauges, like the Regge-Wheeler (RW) one in the case of Schwarzschild black
holes. In this letter we present a new scheme, based on the
Particle-without-Particle formulation of the field equations, where the
gravitational self-force can be obtained from just solving individual wave-type
equations like the master equations of the RW gauge. This approach can help to
tackle the yet unsolved Kerr case.
