- Problem 10 Robertson Walker Metric 25pts Cosmological Principle Is That The Universe Is Composed Of The Homogeneous A 1 (25.29 KiB) Viewed 18 times
Problem 10: Robertson-Walker metric (25pts) Cosmological principle is that the Universe is composed of the homogeneous and isotropic space. One can use the Killing vector fields in order to derive the conditions of static metric with spherical symmetry. ds² = -900(t, r) c² dt² + 2901 (t, r) cdtdr + 911(t, r)dr² + 922(t, r) (d0² + sin² 0do²) (13) Use three Killing vectors for rotations in space as = (0, 0, -z, y), 2 = (0,2,0,-), = (0, -y, x, 0) (14) as well as another three Killing vectors for translational invariant as ni = (0, 1, 0, 0) , ng =(0, 0, 1,0) , ng = (0, 0, 0, 1) (15)