This question involves Minkoski space, which has a line-element that can be written in {t, r, y, } coordinates as ds' = -dt? + dx3 + dy + dz. a) Write down an expression for the tangent vector, t, to a curve in this space that is specified by I" (A) = (t(X), I(X), y(X), z(X)) = (cosh A, sinh ), 0,0) , where > is a parameter along the curve. Write down your answer using the coordinate basis vectors associated with the {t, r, y, >} coordinates. ) Identify whether the curve specified above is space-like, time-like or null, and whether or not it is affinely parameterized. Explain your answers. c) Calculate the length of the curve from part a), between the points labelled A = >, and A = 12. d) Apply a suitable coordinate transformation, from Cartesian to cylindrical coordinates, to show that the line-element for Minkwoski space can also be written as ds' = -dt' + dz' + dr + r'do?. e) Determine which Christoffel symbols will be non-zero, in the cylindrical coordinate system from part d), and give their values. Next, calculate the components of the Riemann curva- ture tensor in the cylindrical coordinate system, and explain how you could have predicted the result you find without having performed any calculations at all. Hint: It will be useful to exploit the symmetries of the Riemann tensor, when performing this calculation