Figure 12

Figure 12: This figure shows the expansion Θ (left scale), and the “generalized expansions” r Θ (left scale) and r2Θ (right scale), for various r = constant surfaces in an Eddington–Finkelstein slice of Schwarzschild spacetime. Notice that all three functions have zeros at the horizon r = 2m, and that while Θ has a maximum at r ≈ 4.4 m, both rΘ and r2Θ increase monotonically with r.