266 DOC. 10 RESEARCH NOTES
[p. 55]
[133]Einstein
computes
the
divergence
ystTrs;
t
of
the
fully
covariant,
antisymmetric tensor
Trs.
The
final
result
is
[eq.
204].
Weiteres
über
Div. des Kov.
Tensors.
T~5~
teres uber
D
a
ax
t
r
t
k*l\
st)
/
\xs
\
r[X
s
&
T darf vertauscht
werden.
T(IV
sei
antis. Punkttensor
Tiiv^iia^vß
kovarianter Tensor
-^po£pH&oa
21 ^iiv^po^pn^oa"
MPG
^
gemischter
Tensor
Spannungs energiet.
217iiv7po£
t
aß/^aii^ßv
21
^aß^aji^ß
v
Ist
0JiV
Punkttensor kovarianter Tensor
zu
T^v
kontravarianter
"
T zu
Punkttensor
X0^6^^
[134]
9
217aß7Vß'Yaa/YßvYß
^
=
t
G
VG
gebildet.
dxn
vn jiV m
[eq.
205]
[eq.
206]
dg
nv
I[135]
är
Vv
=
°- [eq.
207]
*vn
®|iv®p/?^pH
+
^aß-^a'ß,Yaa/TßvYß'n
gmv
d
gmv^vn
0,v0^^p^mv
+
^a^aTYaa^ß^
^ ^
n
d
®(iv^p|i^mvWp
V
^®pn0^ (®nv^|ip^vw)
...(1)
/i
®vn^vp^(im
[134]Einstein
sums
the
terms
[eq.
205]
and
[eq.
206] to give
the
fully
contravariant electro-
magnetic field stress-energy tensor
tvG.
The
G(jv
of
[eq.
205]
is
the
fully
contravariant Max-
well
field
tensor
and the
Taß
of
[eq. 206]
the covariant
tensor
dual
to
it. (Einstein's
notation
in
the lines above
varies from
this.)
This
expression
for
tva
is
a
generalization
(which
omits
a