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 Question wave equation in curved spacetime ( Physics Help and Math Help - Physics Forums Special General Relativity )Updated: 2008-04-20 01:23:57 (4)
 wave equation in curved spacetime Does anyone know how to derive the wave equation in curved spacetime? A reference, or an outline of the derivation would be very helpful. Thanks.
 Answers: wave equation in curved spacetime ( Physics Help and Math Help - Physics Forums Special General Relativity )
wave equation in curved spacetime

 Originally Posted by Antenna Guy Just a guess, but : ?
Nope. That can't work because the left-hand side is a scalar quantity, while the right-hand side is a vector.

 Originally Posted by Antenna Guy [addendeum: or is it ?] Regards, Bill
Not this either. Perhaps it will be simpler if I just state the result and leave the proof as an exercise. Given an orientable Riemannian manifold , one has a preferred idea of a connection in the form of the Levi-Civita connection. This allows one to define, for example, a straightforward notion of covariant differentiation on tensor fields over . The relationship between the covariant divergence of a vector and the partial derivative of the vector is given by

shoehorn

wave equation in curved spacetime

 Originally Posted by shoehorn Given a vector , can you think of any cute expressions for ?
Just a guess, but : ?