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We study the effect of spatially dependent mass function over the solution ofthe Dirac equation with the Coulomb potential in the (3+1)-dimensions for anyarbitrary spin-orbit $\kappa $ state$.$ In the framework of the spin andpseudospin symmetry concept, the analytic bound state energy eigenvalues andthe corresponding upper and lower two-component spinors of the two Diracparticles are obtained by means of the Nikiforov-Uvarov method, in closed form.This physical choice of the mass function leads to an exact analytical solutionfor the pseudospin part of the Dirac equation. The special cases $% \kappa =\pm1$ ($l=\widetilde{l}=0,$ i.e., s-wave)$,$ the constant mass and thenon-relativistic limits are briefly investigated.

Solutions of the spatially-dependent mass Dirac equation with the spin and pseudo-spin symmetry for the Coulomb-like potential