But Pete that section is dealing with an object at rest with respect to an accelerated non-inertial reference frame - that is indistinguishable from a uniform gravitational field - and as AE states a co-ordinate change will create the gravitational field BUT only in a frame that could otherwise be thought of as a non-inertial accelerating frame (K') .

That’s correct. Perhaps you think that the creation of the gravitational field is something which is independent of the coordinate system and intrinsic to spacetime? Many physicists today don’t things which have an existence which is frame dependant.

In fact you said it yourself – Invoke a change in spacetime coordinates from an inertial frame to a non-inertial frame and you can have a gravitational field.

I still do not understand how you could create a grav field with is identical locally to a non-inertial frame (with pseudoforces etc) from an inertial frame via coordinate transformations.

I don’t understand where your confusion lies. You do understand, don’t you, that the term “coordinate transformation” refers to changes in spacetime coordinates between two frames of reference including those changes in reference from an inertial frame of reference to an accelerating frame of reference, right?

Think of this as you would an electric field. If you have a frame of reference in which there is no electric field but there is a magnetic field present then you can change coordinates and “produce” an electric field. In the same way that you can “produce” an electric field by a change in spacetime coordinates you can also change spacetime coordinates to “produce” a gravitational field.

Note #1: Just in case you’re one of those people who think that in relativity there is no such thing as an electric field but only an electromagnetic field then let me warn you that such an assumption is not true. All it means is that the electric field produced is observer dependant. As I recall, the electric field 4-vector is proportional to the contraction of the Faraday tensor, aka the electromagnetic field tensor, and the observer’s 4-velocity.

Note #2: Just because you

*can* produce such things by a change in spacetime coordinates it doesn’t mean that you

*actually do* create such things. Just as you can change from one inertial frame to another in the presence of a magnetic field and produce an electric field it doesn’t mean that just any old change in spacetime coordinates will produce such a gravitational field. Obviously if your in an inertial frame of reference in flat spacetime you can’t produce a gravitational field by invoking a Lorentz transformation. In the same way there are transformations which won’t give you an electric field in certain kinds of magnetic fields.