Theory of the interaction forces and the heat transfer between moving bodies mediated by the fluctuating electromagnetic field

Within the framework of unified approach we study the Casimir-Lifshitz interaction, the van der Waals friction force and the radiative heat transfer at nonequilibrium conditions, when the interacting bodies are at different temperatures, and they move relative to each other with the arbitrary velocity $V$. The analysis is focused on the surface-surface and surface-particle configuration. Our approach is based on the exact solution of electromagnetic problem about the determination of the fluctuating electromagnetic field in the vacuum gap between two flat parallel surfaces moving relative to each other with the arbitrary velocity $V$. The velocity dependence of the considered phenomena is determined by Doppler shift and can be strong for resonant photon tunneling between surface modes. We show that relativistic effects give rise to a mixing of the contributions from the electromagnetic waves with different polarization to the heat transfer and the interaction forces. We find that these effects are of the order $(V/c)^2$. The limiting case when one of the bodies is sufficiently rarefied gives the heat transfer and the interaction forces between a moving small particle and a surface. We also calculate the friction force acting on a particle moving with an arbitrary velocity relative to the black body radiation.