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I'm thinking of a manifold of spacetime. And with acceleration one goes from the initial frame of reference (the first manifold) to a frame of reference traveling with respect to the first frame. This can be viewed as a different manifold but shares some points with the first. Can this acceleration from one frame (manifold) to another frame (manifold) be characterized by numbers that tell us something about the mass or energy need to go from one frame to another? I hope this is enough information to generate answers. Thanks you.