Special relativity in general relativity?

Starting from the metric in harmonic coordinates for a test particle m₁ around a heavy particle $m_2{\mathrm{(m}}_2{\mathrm{\gg m}}_1)$ at rest, the EIH Lagrangian is recovered by making a Lorentz transformation, followed by a canonical transformation and an appropriate symmetrization in the two masses. This raises the question of a special relativity content in general relativity, a feature not directly implied by the general covariance.