ABSTRACT

Near a body of mass M (e.g. the Sun), spacetime is curved. The world lines of particles and light rays in the field of M are geodesics; to find these it is necessary to know the metric tensor gij in some useful coordinate system xi . We choose x0 to be a time variable t, and xl, x2, x3 to be the polar coordinates already introduced, with M at the origin O. Thus we have a series of concentric r-spheres with defined area 4πr 2, each sphere being made of rigid rods arranged in a grid corresponding to latitude and longitude angles θ and ϕ, with clocks at each intersection. If M were zero, the separation formula would be Δ T 2 = Δ t 2 − ( Δ r 2 + r 2 Δ θ 2 + r 2 sin 2 θ Δ ϕ 2 ) / c 2 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742143/f12fe629-b84c-463d-b53e-6adef487b58d/content/eq176.tif"/>