PROBLEM 4 is a A certain spherically symmetric spacetime geometry is described by the following line element, in which constant: dr2 +r? (do? +sinode?) d} =-(4+ ]+ entry * r*(_0? + sinOdo) (a) What are the curves t(r) that describe the light cones in this geometry? Sketch them on a t,r spacetime diagram and draw some of the local light cones in. What happens to the light cones as r - 0? (b) Calculate all of the Christoffel symbols for this spacetime from the geodesic equations (i.e., from applying the Euler-Lagrange equations to the Lagrangian for a timelike free particle).