The strong equivalence principle extends universality of free fall to bodies with appreciable gravitational self-energy, and states that the outcome of any local experiment, including a gravitational experiment, in a freely falling laboratory is independent of its location and velocity. In a sufficiently small freely falling laboratory the external gravitational influence can be removed to first order by choosing a local inertial frame.

This does not remove tidal forces or the Riemann curvature tensor. The laboratory must be small compared with the length scale over which the external gravitational field varies. These qualifications distinguish a local equivalence statement from the incorrect assertion that gravity can be transformed away throughout an extended curved region.