Equivalence of local gravity and acceleration
Acceleration under gravity is independent of any attribute of an object. The experimentally verified equivalence of gravitational and inertial mass implies the equivalence of uniform gravity and accelerated references frames. This chapter shows a coordinate system to analyze tidal forces. The tidal force is the difference in forces experienced by neighboring particles. Such particles could be isolated test particles, or they could be infinitesimal mass elements in an extended object. An initially spherical object would be deformed under tidal stresses: stretched in the radial direction and compressed in the transverse directions—what happens to the oceans on Earth. Every freely falling frame of small size is a local inertial frame, local inertial frame and hence is one in which special relativity (SR) applies, and the spacetime of SR is flat. Thus, in regions of spacetime small enough that gravitational fields are uniform, spacetime is flat. A flat region of spacetime cannot “cover” all of spacetime, which general relativity shows is globally curved.