Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

► The definition of the momentum of light inside matter is studied. ► Fully relativistic analysis of the dielectric “Einstein box” thought experiment. ► Minkowski, Abraham and the total energy-momentum tensors are derived in detail. ► Some assumptions hidden in the usual Einstein box argument are identified. ► The Abraham momentum is not uniquely selected as the momentum of light in this case.