Problem 1 [3] Consider a space-time with line element ds2 = -dt2 + e2*dx2 + dy? + dz2. (i) Show that the 4-vectors eo = (1, 0, 0, 0), ej = (0, e-x, 0, 0), ez = (0, 0, 1, 0) and es = (0, 0, 0, 1) form an orthonormal basis. (ii) Using the local inertial frame given in part (i), compute the components po = -p . e and pl = p . e; of the 4-momentum p = (1, e-x, 0, 0). What is the mass of a particle with this 4-momentum? (iii) In a global frame (t, x), compute the 4-momentum p of a particle (mass m) moving along a worldline given by t(7) = a sinh(ar) , x(7) = log(a cosh(ar)) and y(T) = 0 = z(), with a constant a. Use your result to derive the components p" in the orthonormal basis of part (i)