  A new geometric interpretation for General Relativity (GR) is proposed. We
show that in the presence of an arbitrary affine connection, the gravitational
field is described as nonmetricity of the affine connection. An affine
connection can be interpreted as induced by a frame of reference (FR). Although
the gravitational field equations are identical to Einstein's equations of GR,
this formulation leads to a covariant tensor (instead of the pseudotensor) of
energy-momentum of the gravitational field and covariant conservation laws. We
further develop a geometric representation of FR as a metric-affine space, with
transition between FR represented as affine deformation of the connection.
Geodesic and autoparallel worldlines are considered. We show that the affine
connection of a NIFR has curvature and may have torsion. We calculate the
curvature for the uniformly accelerated FR. Finally, we show that GR is
inadequate to describe the gravitational field in a NIFR. We propose a
generalization of GR, which describes gravity as nonmetricity of the affine
connection induced in a FR. This generalization contains GR as a special case
of the inertial FR.
