Blackbody friction force on a relativistic small neutral particle

The friction force acting on a small neutral particle during relativistic motion relative to the blackbody radiation is calculated in the framework of fluctuation electrodynamics. It is shown that the particle acceleration is determined by the friction force in the particle rest reference frame ($K^{\prime }$ frame), which, in general, is not equal to the friction force in the frame of the blackbody radiation ($K$ frame). The difference between the friction forces in the different frames is connected to the change of the rest mass of a particle due to the absorption and emission of radiation. The friction force in the $K^{\prime }$ frame is determined only by the interaction of a particle with the blackbody radiation. In the $K$ frame the interaction of a particle with its own thermal radiation also contributes to the friction force. For the steady-state temperature of a particle the friction forces in the $K^{\prime }$ and $K$ frames are equal. For an atom the blackbody friction is determined by the electronic linewidth broadening, which is calculated considering the interaction of an atom with its own radiation. In the ultrarelativistic case $\left(1-\beta \to 0\right)$ for an atom the friction force diverges as ${(1-\beta )}^{-3}$, and the (average) temperature of an atom $T_2\approx {(1-\beta )}^{-3/8}{T}_1$, where $T_1$ is the temperature of the blackbody radiation and $\beta =V/c$. Controversies in the theory of the blackbody friction are discussed.