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I'm reading "Relativity: The Special and the General Theory" by Albert Einstein. In the following extract:

Let us consider a space-time domain in which no gravitational field exists relative to a reference-body K. K is then a Galileian reference-body, and the results of the special theory of relativity hold relative to K. Let us suppose the same domain referred to a second body of reference K', which is rotating uniformly with respect to K. We shall imagine K' to be in the form of a plane circular disc, which rotates uniformly in its own plane about its centre. An observer who is sitting on the disc K' is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body K. But the observer on the disc may regard his disc as a reference-body which is “at rest”; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. Nevertheless, the space-distribution of this gravitational field is of a kind that would not be possible in Newton’s theory of gravitation.

footnote: The field disappears at the centre of the disc and increases proportionally to the distance from the centre as we proceed outwards.

Why is the Coriolis force not affecting the gravitational field in the frame K'?

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The Coriolis force is not mentioned above because the disk and the observer are all at rest in the rotating frame. As soon as something is moving in the rotating frame then the Coriolis force will become important.

In the mathematics of general relativity both the centrifugal and the Coriolis forces show up in the Christoffel symbols. So they are both accounted for.

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