264
DOC.10 RESEARCH NOTES
[p. 53]
a
ffoa®
aß
ff
caYgjxYßv
(Yrh^UO)
a
dxß
K'ß»^
Jc^T«ßßdxoay
Divergenz antisymmetrischer
Tensoren
dT..
fdg
[131]
r,
=
S
sü
3xs
+
(y
N
*r
a
s
a
V
3
*
H
r
1
a
3g^ia
2M(dSs
ax
+
3g(15
dx"
dxa
T
r
[IS
Y5a
dgsa
3
ga|i
dx
verschwindet,
wenn
T
antisymmetr.
+
/
dg5(1
3x 3x
a
r[i
fx
&
s
vertauscht
dg
Häx
5
|1
3
g[La
r
rs
dgS[L
I
dTrs
dx
1
3
G
+
^^~T
rs
2
dxs
-
"
ar_"
q
dG
+
-
jG~'rs
3xs 2
JG
dx
rs J-G
a
(J-GTrs)
dxs
[eq.
203]
P
Elektr.
Menge
ist
Skalar
ebenso wahre
el.
Dichte
dxv
. .
p
ds dxv
[132]
0
ds
=
kontravarianter
Vektor
=
Po
=
-o
V
eo
dt
V0ds
J-G
=
p
0J-G
dt
ds
/J^G
dt
ds
p
dxv
P
• •
J^G
dt
-G
ist kontravarianter
Vektor.
Hieraus
Feldgleichungen (1. System.
[131]Einstein
begins
to
develop
a
generally
covariant formulation of
electrodynamics.
The
tensor
Trs
is
contravariant
in
both indices
and is
the
antisymmetric
Maxwell
field
tensor.
Ein-
stein
computes
its divergence,
Trs;s. After reduction the result
is
[eq.
203].
5