Problem 4. (20 pts) TH1 H2 H k in terms (a) (5 pts) Let T denote a (k,l)-type tensor. Please write down the formula for

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Problem 4 20 Pts Th1 H2 H K In Terms A 5 Pts Let T Denote A K L Type Tensor Please Write Down The Formula For 1 (135.34 KiB) Viewed 15 times

Problem 4. (20 pts) TH1 H2 H k in terms (a) (5 pts) Let T denote a (k,l)-type tensor. Please write down the formula for V of , and the Christoffel symbols rp. VVV - (b) (3 pts) Please use the result in part (a) to show that VS = 0, where d is the Kronecker delta function. (c) (5 pts) Consider a metric tensor guv. Use the result in part (b) and the metric compatible condition Γρθμν = 0 to show that Vg¹ = 0, where g is the inverse metric. dxμ Please show (d) (7 pts) Consider a curve in spacetime denoted by x¹(A), with the tangent vector vº that the geodesic equation dλ v²₂v¹ = 0 can be rewritten as dx dx² d² xH dλ² +TH 0. vp ἀλ ἀλ