Bohr model and Quantum Mechanics stabilize the atoms in order to have a minimum state (due to some effective or centrifugal force) avoiding electrons to hit the nuclei. Thus, electrons (accelerated charges) do not emit electromagnetic waves, losing energy until they fall down into the nucleus.
Quantum gravity: we know that classical gravity emitting GRAVITATIONAL waves, inspiral (just like classical atoms emitting electromagnetic waves), but...Shouldn't quantum gravity avoid this? That is, when (small) bodies theoretically approach Planck length, are they stabilized? Should we expect a similar stabilization from quantum gravity? What string theory says about this problem (2 particles, in strong gravity, with a radius when radiation and backreaction are important)? And LQG?