  We show that the acceleration-difference of neighboring free-falling
particles (= geodesic deviation) measured in the local reference frame of a
GR-noninertial observer is not given by the Riemann tensor. With the
gravito-electric field of GR defined as the acceleration of free-falling
quasistatic particles relative to the observer, the divergence of the
gravito-electric field measured in the reference frame of a GR-noninertial
observer is different from the Ricci curvature $R^0_{\,\,0}$. We derive our
exact, explicit, and simple gravito-Gauss law for the divergence of the
gravito-electric field in our new reference frame of a GR-noninertial observer
with his LONB (Local Ortho-Normal Basis) and his LONB-connections in his time
and 3-directions: the sources of the divergence of the gravito-electric field
are contributed by all fields including the GR-gravitational fields,
gravito-electric and gravito-magnetic. In the reference frame of a GR-inertial
observer our gravito-Gauss law coincides with Einstein's $R^0_{\,\,0}$
equation, which does not have gravitational fields as sources. We derive the
gravito-Ampere law, the gravito-Faraday law and the law for the divergence of
the gravito-magnetic field. The densities of energy, momentum, and
momentum-flow of GR-gravitational fields are local observables, but depend on
observer with his local reference frame: these quantities are zero if measured
by a GR-inertial observer. For a GR-noninertial observer the sources of
gravitational energy, momentum, and momentum-flow densities have the opposite
sign from the electromagnetic and matter sources. In the gravito-Gauss law the
sources contributed by gravitational energy and momentum-flow densities have a
repulsive effect on the gravitational acceleration-difference of particles.
