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where
(
)
T
= radiative part
==
TqwawWkk
24 2
22
(34b)
rn
rn
R
()
rn
2
T
=
bounded part
B
rn
=+
TT
rn
rn
()
()
3 4
24
(
)
(
)
(
)
= + + + + ⎣ ⎦
This proves that such parts are dynamically independent, which means
that they verify separately (outside the world line):
qw
g
ka
ka
B kv
kv w
2
12
W kk
1
2
rn
r
n
n
r
r
n
n
r
r
n
n
,
(35a)
T
=
0
rn
,
R
n
T
=
0
(35b
rn
,
B
It is simple to obtain the relations:
(
)
n
TB
,
n
=
λ
B
n
TU
=
λ
U
T
η η
=
2
4
λ
=−
q
/2
w
,
(36)
rn
r
tn
,
r
rn
r
Therefore, we have that a F and r T have the same null proper vectors,
which is a general result (see Synge [27], p. 337). Plebañski [6], p. 41,
was the first one to observe that B r is a proper vector of i T . If we substitute
Eqs. (34b) and (34c) in Eq. (34a), we obtain the Synge [7] compact ex-
pression for the energy tensor associated to the Liénard-Wiechert retarded
potential:
(
)
24
2
2
(37)
TqwkUkU aBkk g
=
+
+
+
1
2
rn
r
n
n
r
r
n
rn
Weert's [30, 31] attention was driven forward to the fact that Eq. (35)
are valid identically , and he therefore suggested the existence of super-
potentials for the bounded and radiative parts. However, he only obtained
successfully the explicit form of the superpotential (which now carries his
name) sar
B
K
which generates the bounded part [32-35]:
 
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