A relativistic model for the extended x-ray-absorption fine structure, in which the energy loss of the emitted photoelectron is accounted for by using a complex energy-dependent exchange-correlation potential, has been developed. Relativistic curved-wave single-, double-, and triple-scattering formulas for excitation from any core hole have been found. The dominant single-scattering signal has been computed for the first shell at the ${\mathit{L}}_{2}$ and ${\mathit{L}}_{3}$ edges of Th (Z=90), Pt (Z=78), and Eu (Z=63) and at the K edge of Sr (Z=38) using this model. Comparisons of the relativistic scattering amplitudes of the Dirac model with the current standard Schr\"odinger curved-wave model reveal that the latter deviates from the more exact Dirac model by 20% above 240 eV for Th, by 15% above 240 eV for Pt, and by 10% above 140 eV for Eu. For lower energies, the deviations are as much as two times larger. Differences between the Dirac model ${\mathit{L}}_{2}$- and ${\mathit{L}}_{3}$-edge amplitudes occur below 240 eV for Th and Pt with values of 2% and 6%, respectively. For Eu, this difference diminishes to 4% and occurs only below 140 eV. In the case of the K edge of Sr, the Schr\"odinger single-scattering amplitude differs from the Dirac amplitude by 5% for energies above 95 eV. The spin dependence of the generalized Ramsauer-Townsend effect is also exhibited.