you are absolutely wrong, Mark! All experts in General Relativity would agree that in GR acceleration is an absolute concept. The concept of an "inertial frame" is a crucial one in GR. An inertial frame is a non-accelerating frame. One can tell by local measurements whether one is in an inertial frame or not. This is non-controversial. Anyone who knows GR understands this. It is true that Einstein was led to GR by Machian ideas, and according to Mach's ideas acceleration is relative. But it is generally agreed by that the theory Einstein actually came up with is NOT Machian. Though he was inspired by Mach's ideas, Einstein's theory does not actually realize Mach's principle of the relativity of acceleration.
Samuel M Barr says:
"you are absolutely wrong, Mark! All experts in General Relativity would agree that in GR acceleration is an absolute concept. The concept of an "inertial frame" is a crucial one in GR. An inertial frame is a non-accelerating frame. One can tell by local measurements whether one is in an inertial frame or not. This is non-controversial. Anyone who knows GR understands this. It is true that Einstein was led to GR by Machian ideas, and according to Mach's ideas acceleration is relative. But it is generally agreed by that the theory Einstein actually came up with is NOT Machian. Though he was inspired by Mach's ideas, Einstein's theory does not actually realize Mach's principle of the relativity of acceleration. "
An inertial frame is a non-accelerating one in general relativity (or any other theory), yes. BUT YOU CAN MAKE ANY FRAME IN THE UNIVERSE A REFERENCE FRAME. and the rest of the universe will accelerate around it and account for the forces which makes the frame you chose a fixed frame. This is the general principle of relativity.
General relativity describes the system (in this case the universe) relative to the rest of the universe from the perspective of the reference frame. Thus relativity.
Mark Wyatt
Samuel Barr says:"All experts in General Relativity would agree that in GR acceleration is an absolute concept."
Another way of putting the same point is to say that, in Newtonian mechanics and special relativity, rotation is “absolute” because the transformations between inertial frames (Galilean or Lorentzian) preserve rotational states. Thus the “absoluteness” of rotation arises precisely from singling out one type of frame, by one type of transformation, instead of allowing arbitrary transformations and arbitrary frames. Einstein held that this epistemological insight had a natural mathematical representation in the principle of general covariance, or the principle that the laws of nature are to be invariant under arbitrary coordinate transformations. More precisely, what this means is that coordinate transformations are no longer required (as in the affine spaces of Newtonian mechanics and special relativity) to take straight lines to straight lines, but only to preserve the smoothness of curves (i.e. their differentiability). The general theory of relativity was intended to be a generally covariant account of spacetime, and its general covariance was intended to express the general relativity of motion. And the theory came into being because Einstein perceived a deep connection between this project and that of finding a relativistic theory of gravitation.
http://plato.stanford.edu/entries/spacetime-iframes/
Mark Wyatt