Angular momentum. Follow the steps in Section 2 of Chapter 4, but again use the rain metric, to derive the expression for angular momentum per unit mass, the second constant of the motion of the stone. Show that the result is exactly the same as for the Schwarzschild metric, namely,
One can go on to describe orbits of particles and light both outside and inside the horizon employing coordinates r, frain, <j>. Derivations are similar to those in Chapters 4 and 5, but the new derivations are complicated by the second term in the equation for energy, above. Rather than pursuing these algebraically complicated derivations here, we look instead at what the plunging rain observer sees as she approaches the crunch point at r = 0.
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