Normal coordinates

At any spacetime point, normal coordinates make the metric equal to the Minkowski metric and all Christoffel symbols vanish at that point.

A Lorentz frame at a spacetime event is an orthonormal tangent basis with metric $\mathrm{diag}(-1,1,1,1)$. Future-oriented frames are related by proper orthochronous Lorentz transformations. Any such basis can be realized at the event by normal coordinates.