The EM-GK isomorphism of gravimagnetics is complete, thus it extends to all the way to the quantum world. The mediator of the gravitational force, the messenger graviton, i.e. virtual graviton, is the analog of the vitual photon. Unlike the photon, and like the virtual photon, the virtual photon carries no gravitational charge. An interesting thing then is the momentum carrying analog to the photon itself.
Regards, Horace Heffner