Consider the Schwarzschild metric denoted by where rs is the Schwarzschild radius, and we have chosen...
Consider the Schwarzschild metric denoted by where rs is the Schwarzschild radius, and we have chosen units c= 1, with the Coordinates .r"-(t.r. θ, φ (a) (5pts) Consider a timelike geodesic a:H(τ), where τ is the proper time lying on the plane θ n/2 with θ Ξ d9/dT 0. Use the Lagrangian L 1μντμχ to derive the cquations governing the geodesic first showing that where E, L arc constants (b) (5pts) Using the results in (a) and cq.(3), show that (c) (5pts) For u 1/r, derive the cquation u su). dch (d) (5pts) By differentiating cq.(5) with respect to φ, and assuming the orbit is not circular, please show that 212 2's where u- 1/r. State which term in this cquation makes it different from an analogous cquation in Newtonian theory.