- #1
Kyrios
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- 0
Homework Statement
Show [itex] U^a \nabla_a U^b = 0 [/itex]
Homework Equations
[itex] U^a [/itex] refers to 4-velocity so [itex] U^0 =\gamma [/itex] and [itex] U^{1 - 3} = \gamma v^{1 - 3} [/itex]
The Attempt at a Solution
I get as far as this:
[itex] U^a \nabla_a U^b = U^a ( \partial_a U^b + \Gamma^b_{c a} U^c) [/itex]
And I think that the Christoffel symbol is 0 in minkowski space so that gives:
[itex] U^a \partial_a U^b [/itex]
And I'm not certain what to do from this point