DivA__:=3∑μ=0∂Aμ∂xμ=∂A0∂jc0t+div→A
where A__ is an arbitrary four-vector
Note 1 to entry: Four-divergence is useful in STR. In general theory of relativity (GTR) for non-flat space-time, a more sophisticated method is used.
Note 2 to entry: The four-divergence of a tensor quantity Q of order n≥1 is a scalar product of four-nabla and that quantity: DivQ=◊⋅Q yielding a tensor quantity of order n−1.
Note 3 to entry: In the International System of Quantities, the dimension of four-divergence is L−1.
Div A _ _ := ∑ μ=0 3 ∂ A μ ∂ x μ = ∂ A 0 ∂j c 0 t +div A → MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaiiraiaacMgacaGG2b WaaWqaaeaacaWGbbaaaiaacQdacqGH9aqpdaaeWbqaamaalaaabaGa eyOaIyRaamyqamaaBaaaleaacaaH8oaabeaaaOqaaiabgkGi2kaadI hadaWgaaWcbaGaaqiVdaqabaaaaaqaaiaaeY7acqGH9aqpcaaIWaaa baGaaG4maaqdcqGHris5aOGaeyypa0ZaaSaaaeaacqGHciITcaWGbb WaaSbaaSqaaiaadcdaaeqaaaGcbaGaeyOaIyRaiyjGbQgacaWGJbWa aSbaaSqaaiaaicdaaeqaaOGaamiDaaaacqGHRaWkcaGGKbGaaiyAai aacAhaceWGbbGbaSaaaaa@5576@
where A _ _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWGbbaaaa aa@347D@ is an arbitrary four-vector
Note 2 to entry: The four-divergence of a tensor quantity Q MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamyuaaaa@347C@ of order n≥1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamOBaiabgwMiZkaaig daaaa@371A@ is a scalar product of four-nabla and that quantity: DivQ=◊⋅Q MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaiiraiaacMgacaGG2b Gaamyuaiabg2da9iabgsSiGlabgwSixlaadgfaaaa@3DA3@ yielding a tensor quantity of order n−1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamOBaiabgkHiTiaaig daaaa@3641@ .
Note 3 to entry: In the International System of Quantities, the dimension of four-divergence is L −1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacaabaaGcbaGaciitamaaCaaaleqaba GaeyOeI0IaaGymaaaaaaa@35AD@ .