**Publication date:** Jul 2018

**Abstract:**

In many astrophysically relevant situations, radiation-reaction forces

acting upon a charge cannot be ignored, and the question of the location

and stability of circular orbits in such a regime arises. The motion of

a point charge with radiation reaction in flat spacetime is described by

the Lorenz-Dirac (LD) equation, while in curved spacetime it is

described by the DeWitt-Brehme (DWB) equation containing the Ricci term

and a tail term. We show that for the motion of elementary particles in

vacuum metrics, the DWB equation can be reduced to the covariant form of

the LD equation, which we use here. Generically, the LD equation is

plagued by runaway solutions, so we discuss computational ways of

avoiding this problem when constructing numerical solutions. We also use

the first iteration of the covariant LD equation, which is the covariant

Landau-Lifshitz equation, comparing the results of these two approaches

and showing the smallness of the third-order Schott term in the

ultrarelativistic case. We calculate the corresponding energy and

angular momentum loss of a particle and study the damping of charged

particle oscillations around an equilibrium radius. We find that,

depending on the orientation of the Lorentz force, the oscillating

charged particle either spirals down to the black hole or stabilizes the

circular orbit by decaying its oscillations. The latter case leads to

the interesting new result of the particle orbit shifting outwards from

the black hole. We also discuss the astrophysical relevance of the

presented approach and provide estimates of the main parameters of the

model.

**Authors:**

Tursunov, Arman; Kološ, Martin; Stuchlík, Zdeněk; Gal’tsov, Dmitri V.;