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Homework Statement
show that the definition of the invariant divergence
divA = 1/√g ∂i (√g Ai)
is equivalent to the other invariant definition
divA = Ai;i
Ai;k = ∂Ai/∂xk + ГiklAl
Гkij = gkl/2 (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl)
Homework Equations
g is the metric tensor
hints from class:
you will have to check that Гlil = 1/√g ∂i√g
you will have to differentiate determinants
write the answer in terms of the derivative of the metric tensor and inverse metric tensor
The Attempt at a Solution
so far I have
divA = ∂Ai/∂xk + (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl)Al
but i don't know if this is correct or where to go from here. Christoffel symbols are new to me, can anyone point me in the right direction?
thanks