no /j /2gaa',gbb' a'/b' (4) dT,
(47)-1 g1/2 (FacFbc
The divergences of these tensors are found to be
-m0 a' g a'b (g1/2(4);b, d
e 12 /2 aF a'b' b'(4)dT
mo J /S2ga'"a'd (4)dT
Fa bb,
(47r) 1 ;b b (Fd;b Fdb;c + Fbc;d) Fcd
-Fabb.
Combining these results, one obtains the conservation law
Ta;b = 0.
Vector potentials and electromagnetic fields.
(2-112)
(2-113)
(2-114)
In the Lorenz gauge
gabAa;b = 0,
(2-115)
the electromagnetic field equation (2-107) may be rewritten as an inhomogeneous
vector wave equation
(2-116)
Particular solutions of this equation are given by
where
Tab
particle
Trab
field
1 ab aFcdF
4 )
(2-110)
(2-111)
rab
particle;b
47a g12 (gbcAabc RabA b)