Christoffel symbols. This is known in relativity physics as the "comma to semi-colon rule". So, for example, if in SR, then in GR. On a (1,0)-tensor or 4-vector this would be: On a (2,0)-tensor this would be: Usage The 4-gradient is used in a number of different ways in special relativity (SR): Throughout this article the formulas are all correct for the flat spacetime Minkowski coordinates of SR, but have to be modified for the more general curved space coordinates of general relativity (GR). As a 4-divergence and source of conservation laws Divergence is a vector operator that produces a signed scalar field giving the quantity of a vector field's source at each point. Note that in this metric signature [+,−,−,−] the 4-Gradient has a negative spatial component. It gets canceled when taking the 4D dot product since the Minkowski Metric is Diagonal[+1,−1,−1,−1]. The 4-divergence of the 4-position gives the dimension of spacetime: The 4-divergence of the 4-current density gives a conservation law – the conservation of charge: This means that the time rate of change of the charge density must equal the negative spatial divergence of the current density . In other words, the charge inside a box cannot just change arbitrarily, it must enter and leave the box via a current. This is a continuity equation. The 4-divergence of the 4-number flux (4-dust) is used in particle conservation: This is a conservation law for the particle number density, typically something like baryon number density. The 4-divergence of the electromagnetic 4-potential is used in the Lorenz gauge condition: This is the equivalent of a conservation law for the EM 4-potential. The 4-divergence of the transverse traceless 4D (2,0)-tensor representing gravitational radiation in the weak-field limit (i.e. freely propagating far from the source). The transverse condition is the equivalent of a conservation equation for freely propagating gravitational waves. The 4-divergence of the stress–energy tensor as the conserved Noether current associated with spacetime translations, gives four conservation laws in SR: The conservation of energy (temporal direction) and the conservation of linear momentum (3 separate spatial directions). It is often written as: where it is understood that the single zero is actually a 4-vector zero . When the conservation of the stress–energy tensor for a perfect fluid is combined with the conservation of particle number density (), both utilizing the 4-gradient, one can derive the relativistic Euler equations, which in fluid mechanics