Einstein’s accelerated reference systems and Fermi–Walker coordinates

We show that the uniformly accelerated reference systems proposed by Einstein when introducing acceleration in the theory of relativity are Fermi-Walker coordinate systems. We then consider more general accelerated motions and, on the one hand we obtain Thomas precession and, on the other, we prove that the only accelerated reference systems that at any time admit an instantaneously comoving inertial system belong necessarily to the Fermi-Walker class.