The Newtonian limit of spacetimes describing uniformly accelerated particles

We discuss the Newtonian limit of boost-rotation symmetric spacetimes by means of the Ehlers’ frame theory. Conditions for the existence of such a limit are given and, in particular, we show that asymptotic flatness is an essential requirement. Consequently, generalized boost-rotation symmetric spacetimes describing particles moving in uniform fields will not possess such a limit. In the cases where the boost-rotation symmetric spacetime is asymptotically flat and its Newtonian limit exists, then the (Newtonian) gravitational potential agrees with the potential suggested by the weak field approximation. We illustrate our discussion through some examples: the Curzon-Chazy particle solution, the generalized Bonnor-Swaminarayan solution, and the C metric. PACS: 04.20.Jb, 04.25.Nx, 04.20.Cv