where ds is the spacetime interval
, t represents the proper time of a stationary clock at spatial infinity, (r, [theta], [phi]) are the usual spherical coordinates (2[pi]r being the circumference of a circle at radius r).
If you square this number, you will get a negative real number which when added to the squares of the spatial separations of the event will reproduce the spacetime interval
of special relativity.
515); more emphatically, they claim that 'the diffeomorphism is the counterpart of Leibniz's replacement of all bodies in space in such a way that their relative locations are preserved', because arbitrary diffeomorphisms do not change the 'relative properties [of bodies], such as the spacetime interval
separating them and their relative velocities upon collision' (p.