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We consider the interpretation of tetrad fields as reference frames inspacetime. Reference frames may be characterized by an antisymmetricacceleration tensor, whose components are identified as the inertialaccelerations of the frame (the translational acceleration and the frequency ofrotation of the frame). This tensor is closely related togravitoelectromagnetic field quantities. We construct the set of tetrad fieldsadapted to observers that are in free fall in the Schwarzschild spacetime, andshow that the gravitational energy-momentum constructed out of this set oftetrad fields, in the framework of the teleparallel equivalent of generalrelatrivity, vanishes. This result is in agreement with the principle ofequivalence, and may be taken as a condition for a viable definition ofgravitational energy.

On reference frames in spacetime and gravitational energy in freely falling frames