Motion of point charge with radiation reaction in flat spacetime is described by Lorenz-Dirac (LD) equation, while in curved spacetime - by DeWitt-Brehme (DWB) equation containing the Ricci term and the tail term. I will show that for the motion of elementary particles in vacuum metrics the DWB equation can be reduced to the covariant form of LD equation and covariant Landau-Lifshitz (LL) equation. In the ultrarelativistic case, identical results of integration of LD and LL equations imply the smallness of the third-order Schott term. As an example, I will demonstrate the trajectories of radiating charged particles orbiting Schwarzschild black hole immersed into external asymptotically uniform magnetic field. Depending on the orientation of Lorentz force, the charged particle either spirals down to the black hole, or stabilizes the motion by decaying its oscillations. The latter case leads to an interesting new effect of shifting of the orbit of charged particle outwards from the black hole. I will also discuss the astrophysical relevance of the presented approach and show the estimates of the main parameters of the model applied to some particular black hole candidates.

In General Relativity, it is known that a particle moving in curved spacetime undergoes a force which results from the interaction of the particle with its own field; namely, a self-force or radiation reaction force. In this talk, I discuss the effects of the self-force on the orbital motion of a small object about a black hole: e.g. a test particle orbiting a small black hole (of about a solar mass), a small black hole (of about a solar mass) orbiting a supermassive black hole (of about a million solar masses), etc.. This study can be applied to construction of accurate theoretical gravitational waveforms from binary systems consisting of a small black hole and a supermassive black hole (so called extreme-mass-ratio binaries), which are possible target sources of gravitational waves for eLISA detection.