Consider the following 4D curved spacetime metric ds2 = ea(rt) at2-eB(rit) dr2 -r2 [do2 + sin20 do2] where a(r ,t) and B(r, t) are given functions of r and t. Calculate: (a) All non-zero components of the Riemann curvature tensor. (b) All non-zero components of the Ricci curvature tensor. (c) The Ricci curvature scalar. Hints: The Riemann curvature tensor is defined as Ro or ua aruv + rare axv ev un - rare and JoeRuva = Rouva. Its main properties are: Ruvio = Rouv (symmetric) Ruvio = - Ruvon (anti-symmetric) Ruvio = - Ryuon (anti-symmetric) Ruvio + Rulov + Ruova = 0 (cyclic identity) The Ricci tensor and scalar are given by Ruv = g Rouva and R = guy Ruv . Extra Credit 1: Describe reasons for the splitting of the Riemann tensor into the Ricci and Weyl tensors - no math, words only! (5 points)