It is possible to draw world-lines of the two twins in the non-accelerating one (A) frame of ref. The aging of the other (B), with respect to the first, is evaluated integrating its proper time differential (and comparing it with A's proper time). My question is (certainly already asked): is there a difference, about our ability to draw those diagrams and make that computation, if B accelerates because of a star's gravitational field and not because of his rocket's engines? Could we avoid knowing GR and using SR only, in this case? If the answer is yes, in which other cases (where B is accelerating) would be possible to use SR only?