# Is there a gravitational radiation reaction force?

As you may know, the linearized relativity theory (or gravitoelectromagnetism), obeys equations analogous to Maxwell's equations in electrodynamics. These equations in ED result in the troubling phenomenon of radiation reaction force when the accelerating charge sort of interacts with its own EM radiation field. So, I am asking, is there a similar phenomenon in relativity theory that mass interacts with its own gravitoelectromagnetic radiation field?

Certainly there must be, at least in the linearized gravity, since the mathematics is the same. I guess the situation is solved in general relativity somehow? Finally, is the phenomenon connected to the origins of inertia?

Understanding both is necessary to model gravitational wave sources, particularly in the "extreme high mass ratio limit" where $M_1 ~10^7$ solar masses and $M_2 ~ 1$ solar mass. This should realistically describe the case of, say, a stellar mass black hole merging with one of the supermassive black holes at the centre of a galaxy.