(a) Find an expression for the coordinate speed of light in the ϕ-direction.
(b) Consider Eq. (17.26) in the limit that the particle's mass goes to zero and its speed approaches that of light. Use your result for part (a) to show that r=1.5RS for the circular orbit of a photon around a black hole.
(c) Find the orbital period (in coordinate time t) for this orbit around a 10M⊙ black hole.
(d) If a flashlight were beamed in the ϕ-direction at r=1.5RS, what would happen? (The surface at r=1.5RS is called the photon sphere.)