250
DOC.10
RESEARCH NOTES
[p.
41]
1
2
VA
Ög'K
^A,^
S
g,'K3x_
2?'
/3JC_
[109]
[eq. 156]
d'UdU
d
dU dU
1
d
dU
(
dx2v
dxo dxv
K
dxv
dxa
[eq.
157]
2
3xa
3xv
3
8(K
3#|K
3
/
2
G
2
\
V V
3x.
2
9xg ^ 3xv
y
[eq.
158]
-,
d f^SiK^SiK
[eq.
159]
I
j-
iKV
\
M.
J
-^x
IKV
3
fd8ikV
3
r
3g(K
3Y(K
Yvöyaß37" 3^
2
~
3x^
G V
w-~v
y
[eq. 160]
T^2/3^3^
1
G
(U
muss
verschwinden.)
\
v
V
P
/
IK
^
£/lC
3
Y.hv3*
3xg
3Xv
Y,
3S«K
3
3xv
^
dxa
dx^ j 3x^ dxv
v
\
[110]
3xG
V
y
3y
WennX"§£
=
0
^SiK
^
S/K
dxvdxG
zweiter
Tensor
transformiert
(kGa
d
dxa
)
[109]Following
the
method of
Einstein and
Grossmann
1913 (Doc.
13),
part
1,
§5,
Einstein
seeks
to
find the stress-energy
tensor
for
the gravitational field
associated
with the gravitation
tensor Ag.
-8.
AU
introduced
on
[p. 39]. [Eq. 156]
is the gravitational
force
density acting
on
the
source masses.
It is
to
be expanded
into
the divergence
of
an
expression in
giK
and
U,
which
is
then identified
as
the stress-energy
tensor
of
the
gravitational
field.
The
first and
sec-
ond
terms equal
[eq.
158]
and
[eq. 157] to
second-order
quantities and the final
result
is
given
in
[eq.
159]
and
[eq. 160].
[110]A
similar calculation
is
carried
out
for
the gravitation
tensor
Y^v£/K ^v.