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Eqs. (2.3) and (3.2). Substituting Eq. (29a) into Eq. (11a), we obtain the
matching Faraday's tensor decomposition Eq. (25a) with
FAA
=−
,
(29b)
i
=
1, 2
()
bc
c b
,
b c
,
i
i
i
which means that each part of m F has its own four-potential. Finally, it can
be verified that Eq. (29a) does not satisfy the Lorenz-Riemann condition
(11f):
r
r
2
AAq
=−
=−
0
,
r
,
r
(29c)
1
2
6.2.4 ENERGY-MOMENTUM TENSOR
Now we shall consider the Maxwell tensor r T through which an electro-
magnetic field's content of energy momentum is quantified:
(
)
T
=
F F
c
+
*
F
*
F
c
,
(30a)
1
2
ab
ac
b
ac
b
This satisfi es
TT
=
Symmetry
(30b)
ab
ba
r
T
=
0
Null trace
(30c)
(
)
c
mn
TT
=
1
4
T T
g
Rainich identity
(30d)
ac
b
mn
ab
Symmetry Eq. (30b) is a property of every energy tensor, Eq. (30c) tells
us that the field is made of particles with null mass at rest, photons in this
case; Eq. (30d) was obtained by Rainich [15].
If we employ Eq. (17a) in the second term of Eq. (30a), we obtain an
alternative expression for the Maxwell tensor:
(
)
c
TFF F g
=
1 /4
;
(30e)
ab
ac
b
ab
Substitution of Eqs. (21d) and (25) in Eq. (30e) results in the important
Teitelboim splitting [3]:
 
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