dilation) causes her to receive Terence's communications later and later as measured on her clock, and she never receives any communications from Terence after 100 hours on his clock (dashed green lines). After 100 hours according to Terence's clock, Stella enters a dark region. She has traveled outside Terence's timelike future. On the other hand, Terence can continue to receive Stella's messages to him indefinitely. He just has to wait long enough. Spacetime has been divided into distinct regions separated by an apparent event horizon. So long as Stella continues to accelerate, she can never know what takes place behind this horizon. Introduction to curved spacetime Basic propositions Newton's theories assumed that motion takes place against the backdrop of a rigid Euclidean reference frame that extends throughout all space and all time. Gravity is mediated by a mysterious force, acting instantaneously across a distance, whose actions are independent of the intervening space. In contrast, Einstein denied that there is any background Euclidean reference frame that extends throughout space. Nor is there any such thing as a force of gravitation, only the structure of spacetime itself. In spacetime terms, the path of a satellite orbiting the Earth is not dictated by the distant influences of the Earth, Moon and Sun. Instead, the satellite moves through space only in response to local conditions. Since spacetime is everywhere locally flat when considered on a sufficiently small scale, the satellite is always following a straight line in its local inertial frame. We say that the satellite always follows along the path of a geodesic. No evidence of gravitation can be discovered following alongside the motions of a single particle. In any analysis of spacetime, evidence of gravitation requires that one observe the relative accelerations of two bodies or two separated particles. In Fig. 5-1, two separated particles, free-falling in the gravitational field of the Earth, exhibit tidal accelerations due to local inhomogeneities in the gravitational field such that each particle follows a different path through spacetime. The tidal accelerations that these particles exhibit with respect to each other do not require forces for their explanation. Rather, Einstein described them in terms of the geometry of spacetime, i.e. the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that result in the appearance of a gravitational force acting at a long range from