246
DOC.
10
RESEARCH NOTES
Gleichungen
2kk
d2§im
3x
=
*P0
dx:
dx
m
[102]
ds ds
8a8
mm
[eq. 144]
k
32g-
dg-
°im oim v
Kim
o
Kim
"
d
rfSim
dgim
|
1
d (d2g2
\
°im
_dxK
V
dxK
dxa
J
2dxa
K
^XK
J
[eq. 145]
Energie-
& Impulssatz gilt
mit
der
in Betr.
kommenden
Annäherung.
Eindeutigkeit
&
Nebenbedingungen
tt;
to
Sim
=
dx:
dxm
m
®dxx
dxx
Kontinuitätsbedingung
Po
1
-
[103]
icdt
=
du
[eq.
146]
Dichte materieller Punkte
/
\
IC
d
dt
Poic
1
-
q
V
c2/
/ \
3
dx
Po?
V
+
•
+
[eq.
147]
72
_
dt 1-^r
=
dx
/
3
3 3
[eq.
148]
Tx
(poro^
+
dy
(po^}
+
'
+
Tu
(p0m«} =
0
Beide
obige Bedingungen
sind
aufrecht
zu
erhalten.
3 3
[eq. 149]
Tx
(p0»x»x)
+
3^
(P0»,»y)
+
'
+
Pnrc
* 0
0"^
dx P()
' dy
P
Did,
"Dt
y IC
m
to
u
2g^Iä^(Pommrn)uxmuxm
^
V
m
\
/
2IPo
3m;
ro
m
m
3xm
L-I
[101]The
harmonic coordinate
condition of
[p.
37]
is
yKl
(2giK,
l
-
gKl
i)
=
0.
In
the weak
field
approximation
in
which the
field
components
differ
only
in
first-order
quantities
from
a
diagonal
matrix,
the harmonic
condition
can
be
written
as [eq.
142].
Einstein
conjectures
that
it
can
be
decomposed
into
the
two
conditions
[eq. 143].
[102][Eq.
144]
is
the first-order
gravitational
field
equation
for the weak
field
for
a
gravita-
tion
tensor equal to
gim,
KK
to
first
order and
whose
source masses are
pressureless
dust.
[Eq.
145]
is
an
identity in
second-order
quantities
which
expresses energy-momentum
con–