Question: In Newtonian physics, all reference frames that are in free fall are equivalent, and approximately what?
About the article "General relativity", section "Relativistic generalization".

Candidate passages:
As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.
In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics.
(The defining symmetry of special relativity is the Poincaré group which also includes translations and rotations.)
The differences between the two become significant when we are dealing with speeds approaching the speed of light, and with high-energy phenomena.
With Lorentz symmetry, additional structures come into play.
They are defined by the set of light cones (see the image on the left).
The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image).
These sets are observer-independent.
In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space–time's semi-Riemannian metric, at least up to a positive scalar factor.
In mathematical terms, this defines a conformal structure.
Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected.
Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames.
Instead there are approximate inertial frames moving alongside freely falling particles.
Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.
A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames.
But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf.
below).
The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.
The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.
The same experimental data shows that time as measured by clocks in a gravitational field—proper time, to give the technical term—does not follow the rules of special relativity.
In the language of spacetime geometry, it is not measured by the Minkowski metric.
As in the Newtonian case, this is suggestive of a more general geometry.
At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian.
Consequently, we are now dealing with a curved generalization of Minkowski space.
The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric.
Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).
According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation: The principle of simplicity can be used within Newtonian physics as well as in special relativity; see Nagel and also Blagojević.
In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment (otherwise the differences would set up an absolute standard reference frame).
According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup.
In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries. 
A comparison can be made between Newtonian relativity and special relativity.
Some of the assumptions and properties of Newton's theory are: The existence of infinitely many inertial frames.
Each frame is of infinite size (covers the entire universe).
Any two frames are in relative uniform motion.
(The relativistic nature of mechanics derived above shows that the absolute space assumption is not necessary.)
The inertial frames move in "all" possible relative uniform motion.
There is a universal, or absolute, time.
Two inertial frames are related by a Galilean transformation.
In all inertial frames, Newton's laws, and gravity, hold.
In comparison, the corresponding statements from special relativity are as follows: Rather than allowing all relative uniform motion, the relative velocity between two inertial frames is bounded above by the speed of light.
Instead of universal time, each inertial frame has its own time.
The Galilean transformations are replaced by Lorentz transformations.
In all inertial frames, "all" laws of physics are the same.
Notice both theories assume the existence of inertial frames.
In practice, the size of the frames in which they remain valid differ greatly, depending on gravitational tidal forces.
In the appropriate context, a "local Newtonian inertial frame", where Newton's theory remains a good model, extends to, roughly, 107 light years.
In special relativity, one considers "Einstein's cabins", cabins that fall freely in a gravitational field.
According to Einstein's thought experiment, a man in such a cabin experiences (to a good approximation) no gravity and therefore the cabin is an approximate inertial frame.
However, one has to assume that the size of the cabin is sufficiently small so that the gravitational field is approximately parallel in its interior.
This can greatly reduce the sizes of such approximate frames, in comparison to Newtonian frames.
For example, an artificial satellite orbiting around earth can be viewed as a cabin.
However, reasonably sensitive instruments would detect "microgravity" in such a situation because the "lines of force" of the Earth's gravitational field converge.
In general, the convergence of gravitational fields in the universe dictates the scale at which one might consider such (local) inertial frames.
For example, a spaceship falling into a black hole or neutron star would (at a certain distance) be subjected to tidal forces so strong that it would be crushed.
In comparison, however, such forces might only be uncomfortable for the astronauts inside (compressing their joints, making it difficult to extend their limbs in any direction perpendicular to the gravity field of the star).
Reducing the scale further, the forces at that distance might have almost no effects at all on a mouse.
This illustrates the idea that all freely falling frames are locally inertial (acceleration and gravity-free) if the scale is chosen correctly. 
An observational frame of reference, often referred to as a "physical frame of reference", a "frame of reference", or simply a "frame", is a physical concept related to an observer and the observer's state of motion.
Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized "only by its state of motion".
However, there is lack of unanimity on this point.
In special relativity, the distinction is sometimes made between an "observer" and a "frame".
According to this view, a "frame" is an "observer" plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector.
See Doran.
This restricted view is not used here, and is not universally adopted even in discussions of relativity.
In general relativity the use of general coordinate systems is common (see, for example, the Schwarzschild solution for the gravitational field outside an isolated sphere).
There are two types of observational reference frame: inertial and non-inertial.
An inertial frame of reference is defined as one in which all laws of physics take on their simplest form.
In special relativity these frames are related by Lorentz transformations, which are parametrized by rapidity.
In Newtonian mechanics, a more restricted definition requires only that Newton's first law holds true; that is, a Newtonian inertial frame is one in which a free particle travels in a straight line at constant speed, or is at rest.
These frames are related by Galilean transformations.
These relativistic and Newtonian transformations are expressed in spaces of general dimension in terms of representations of the Poincaré group and of the Galilean group.
In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations.
An example is an observational frame of reference centered at a point on the Earth's surface.
This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the Coriolis force, centrifugal force, and gravitational force.
(All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.)
In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.
All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration.
Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity).
In general relativity, in any region small enough for the curvature of spacetime to be negligible, one can find a set of inertial frames that approximately describe that region.
Physical laws take the same form in all inertial frames.
By contrast, in a non-inertial reference frame the laws of physics vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.
For example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating.
Someone rotating with the Earth must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion.
Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force.