- #1
loops496
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Homework Statement
Suppose [itex]v^\mu[/itex] is a Killing Vector field, the prove that:
[tex]v^\mu \nabla_\alpha R=0 [/tex]
Homework Equations
1) [itex]\nabla_\mu \nabla_\nu v^\beta = R{^\beta_{\mu \nu \alpha}} v^\alpha[/itex]
2) The second Bianchi Identity.
3) If [itex]v^\mu[/itex] is Killing the it satisfies then Killing equation, viz. [itex] \nabla_\mu v_\nu - \nabla_\nu v_\mu=0[/itex]
The Attempt at a Solution
I know I should use normal coordinates making my life easier with the Christoffels and use the that the Riemann tensor appears when I have two covariant derivatives acting on a vector field, but I'm stuck and can't figure out how to proceed :(. Any help will be greatly appreciated.
M.
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