Clarifying some common misconceptions about gravitational effects in free falling frames

Abstract

It is often stated that in free falling systems, locally, the effects of gravity can be ‘transformed away’.
This statement is part of many, even authoritative, versions of the so-called ‘Strong Equivalence Principle’.
Gravitational effects, however, cannot be completely ‘transformed away’ in free falling systems.
In fact, it is well known and generally remarked in the literature that there are (usually tiny) gravitational effects related to the second derivatives of the components of the metric tensor that are not eliminated even in free falling systems.
But the misconception is worsened by the fact that there are other fundamental gravitational effects that also occur in free falling systems, which we focus on in this paper.
Firstly, the gravitational slowing of time: a fact fundamental to the operation of the Global Positioning System, the occurrence of which in free falling systems subject to gravitational acceleration is generally explained by invoking the axiom that acceleration does not affect the flow of time (the so-called ‘clock hypothesis’).
Secondly, there is a gravitational effect on space, dual to that on time and consisting of its stretching (as has been shown elsewhere), which is equally present in free falling frames.
We will show here that it is possible to deduce the presence of these gravitational effects on time and space in free falling systems as well, directly from the metric, thus clarifying that neither the small gravitational effects related to the curvature of spacetime nor the fundamental gravitational effects on time and space can be eliminated in free falling systems. 
In the latter, only gravitational acceleration is actually ‘transformed away’, making them particular inertial frames; the Equivalence Principle (without the designation ‘Strong’ anymore) should be limited to stating this.