And this formula applies equally to the angle between a direction and the outward or the inward radius [since sin(^ - û) = sin û]. We see from Fig. 11.6 that if a photon is emitted at an r-value greater than 3m in an outward direction (r > 0), it will go to infinity. But if emitted inwards, its fate depends on the angle û which the initial direction makes with the inward radius. For large k2-values (small û) it falls into the horizon; for small k2-values (large û) it gets scattered. If the photon is emitted at an r-value less than 3m in an inward direction, it will go through the horizon. But if emitted outwardly, it will go to infinity for large k2 (small û ); for small k2 (large û ) it will attain a maximum radius, turn back and spiral into the horizon. In both cases the critical k2-value is k2 = Vmax = 1 /27m2, and so, by (11.60), the critical û-value is given by
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