In many books, a truth of gravitation field has been stated in the following way: "No matter what mass does matter have, all objects will follow exactly the same trajectory under the action done by gravitation field if they start with the same initial conditions."
But we know, if we state a truth of physics, we must say at first what reference frame we are using. Then what reference frame are we using here to state this truth? Inertial or non-inertial?