Charge displaced in a relativistic electron gas by a weak local potential

March and Murray derived a nonlocal theory of the charge displaced in a nonrelativistic electron gas by a weak, local potential V(x), using the density-matrix theory. The present work, based on the one-electron Dirac relativistic wave equation, generalizes their result to take account of the finiteness of the velocity of light. As examples, when V(x) is slowly varying the linearized version of the relativistic Thomas-Fermi theory of Vallarta and Rosen is recovered, while for weak but localized V(x) the nature of the Friedel oscillations far from the scattering center is derived.