Find an expression for acceleration a of a stationary observer in Schwarzschildspacetime and show that generally it does not vanish (as it would for a stationaryobserver in Newtonian gravitation). Show that the length (a · a)^1/2 of the acceleration4-vector for a stationary observer tends to infinity at the Schwarschild radius,implying that infinite acceleration is required to remain stationary at the event horizonof a spherical black hole. Hint: In flat spacetime, or a local inertial frame, wemay define acceleration as the derivative of the 4-velocity with respect to propertime.