The schwarzschild metric external to a non-spinning spherical mass is -1 2m 2m 1- ds2 r2 (d0sin2 0dp2) dr2 dt2 1- where m is the mass of the body. (note that we are working in units where the speed of light c unity and the gravitational constant g are equal to (iii show from the metric that the proper time of a stationary clock far from the mass coincides with the coordinate t. show from the metric that the circumference of a great circle at radius r is just given by 27r (iv) a pulse of light is emitted radially by a by a stationary observer at radius r2. how long will it take the pulse to make the trip according to the observer at radius r2? you may assume that m/r < < 1. stationary light source at radius ri and detected (v) the observer at radius r2 uses a tape measure to directly measure the distance from ri to r2. using this result, what does this observer conclude was the average speed of the pulse