Self-consistent orbital evolution of a particle around a Schwarzschild   black hole
  The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history of the particle and is difficult to evaluate. As a result, all existing self-force evaluations in curved spacetime are for particles moving along a fixed trajectory. Here, for the first time, we overcome this long-standing limitation and present fully self-consistent orbits and waveforms of a scalar charged particle around a Schwarzschild black hole. 
Peter Diener, Ian Vega, Barry Wardell, Steven Detweiler
gr-qc