10.
Research Notes
on a
Generalized
Theory
of
Relativity
ds2
=
YjG\\xdx\dx
X
2
X
3
X
4
x1 »11 «21 «31 «41
x2
»12
x3
«13
x4
«14
[ca.
August
1912]
Jt, Xo
Xi
X,
[1]
[2]
1
[p.
1]
X
Pi.
ß
12
ß
13
ß
14
II
G^dxxdx]l =
II
G'podx'pdx'a
^X[L p5ap\a5\i
P
*
G'
ol^OC
"rdxrdxr
PG
pT|
GL,
T1 C,
X
'
=
Y
a
jc
r
Lm4
rs s
analog
GV
=
II5p.ßp^
P
O
d
dxs
II
-M
a
""dx'
r
Spezialfall
für die
Gj[3]
G11
G12
G13
G14
1
0 0 0
0
1
0
0
0 0
1
0
0 0 0
c2
[eq. 1]
cAc
- ^grad2c
[4]
2
c
de
dx
de 2
d2c
2(^0
+
2c--
dx
dx
A
(c2)
=
2grad2c
+ 2cAc
grad
(c2)
=
2cgradc
=
Y
Ay
=
grad
2c
+
cAc
grady
=
cgradc
c2
grad
y
2y~
=
grad
2c
3
grad2r
[eq.2]
iY
4
y