The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is
![del _mu=[1/cpartial/(partialt); partial/(partialx); partial/(partialy); partial/(partialz)],](/images/equations/GradientFour-Vector/NumberedEquation1.svg) |
which can be written
 |
where 
is the d'Alembertian.
Gradient Four-Vector
See also
d'Alembertian, Gradient, Tensor, VectorExplore with Wolfram|Alpha
References
Morse, P. M. and Feshbach, H. "The Differential Operator
."
§1.4 in Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 31-44, 1953.Referenced on Wolfram|Alpha
Gradient Four-VectorCite this as:
Weisstein, Eric W. "Gradient Four-Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GradientFour-Vector.html