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A relativistic generalisation of the Hohenberg-Kohn-Sham theory of the inhomogeneous non-relativistic electron gas is presented. In a local scheme, where the results of the homogeneous electron gas are used as input, a self-consistent one-particle Dirac-like equation is derived. When only 'exchange' energy is used as an approximation, the usual Slater's rho 1/3 theory is shown to need a relativistic correction.
A. K. Rajagopal (Sun,) studied this question.