The principle of general covariance from the Equivalence Principle (EEP) tells us that there is no way in principle to locally distinguish between an inertial acceleration and the effects of a gravitational field. When general covariance is expressed in tensorial form we find that if the equation holds true in an inertial frame that it must hold true in a non-inertial frame of reference.
My question is, if the above is true, is a gravitation field just an illusion? Why do we have to consider a gravitational field at all. Why not think of gravity as the effect of the bending of space and time, with gravitation revealed as an illusion, a by-product of geometry. I feel it is the presence of matter that warps space around it, giving us the illusion that there is a gravitation force pulling on neighboring objects.