We can write the geodesic condition as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d^2 x^\alpha}{d\tau^2}={-\Gamma^\alpha}_{\mu\nu}\frac{dx^\mu}{d\tau}\frac{dx^\nu}{d\tau}[/tex]

On the RHS we have two contravariant vectors ( or (0,1) tensors ) contracted with the connection. But the connection is NOT a tensor. So is the LHS a vector? And if so, how does that work?

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# Is acceleration due to gravity a 4-vector?

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