In general, the Christof-fel symbols are de ned as 2 g g x + g g : (28) The Christo el symbols for the perturbed FRW metric in Newtonian gauge are therefore given by 0 00. RiemannChristoffel curvature tensor and the energymomentum tensor of a perfect fluid. 1 1 Tror c(1 - kr2) -aar2 rr (aar sin) å r Imir rr kr 1 kr2 Ice -r(1 kr2) 160 -r(1 kr2) sin 0 ca (47) å 1 176. at perturbed FRW metric, keeping only scalar perturbations, is given by g00 1 2 g0i 0 gij a2 ij1 + 2 : (27) Let us compute the Christo el symbols for this metric. ing expressions for the Christoffel symbols of the FLRW metric, the. I do not see the derivative of another one of the coordinates in the second term, so when attempting to discern the Christoffel symbols by comparing the equation to the geodesic equation, I do not know what the. Ask Question Asked 10 years, 2 months ago. $\alpha=1$ because of the second derivative of $x$ in the equation, $\beta=1$ because of the first derivative of $x$ in the second term, but I do not know what $\gamma$ is. FRW Christoffel Symbols: For the FRW metric, ds2 -c-dt + a(t) + a(e) (1 - ri 1 dr2 + pado+p2 sin0d02 1 kr2 (46) There are 4 rows of Christoffel symbols, 13 in total. Trouble with calculating Christoffel symbols of FLRW metric using Lagrangian method. The FLRW metric which I am using is $$ds^2 = dt^2 - \frac$$ FRW Christoffel Symbols: (Graded) For the FRW metric, d s 2 c 2 d t 2 + a (t) 2 (1 k r 2 1 d r 2 + r 2 d 2 + r 2 sin 2 d 2) There are 4 rows of Christoffel symbols, 13 in total.
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