Virtual particles are the generalisation to all quantum fields of what near-field is in radio to just photons. It's where you don't really benefit much from even calling things "particles" in the first place, because the wave function itself is a much better description.

Unfortunately the maths of QM doesn't play nice with the maths of GR, which is also why zero-point effects are either renormalised to exactly zero or otherwise predict an effect 10^122 times larger than observed.