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I would like to generically describe a 4-vector locally in space-time. Would i go about that by simply taking a 4-vector and multiplying it by a metric? like

[tex] u^{\alpha}=u_{\beta}g^{\alpha\beta} [/tex]

with [tex]u^{\alpha}[/tex] the new 4-vector in the space specified by the metric?

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# Describing 4-vectors in space-time

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