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.;