Four-gradient

In differential geometry, the four-gradient (or 4-gradient) ${\displaystyle \mathbf {\partial } }$ is the four-vector analogue of the gradient ${\displaystyle {\vec {\mathbf {\nabla } }}}$ from Gibbs-Heaviside vector calculus.

In special relativity and in quantum mechanics, the four-gradient is used to define the properties and relations between the various physical four-vectors and tensors.

This article uses the (+,-,-,-) metric signature and tensor index notation in the language of 4-vectors.

SR and GR are abbreviations for Special Relativity and General Relativity respectively.

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