D O C . 3 2 C A L C U L A T I O N S 6 5
32. Calculations R×μν
[Berlin, after 18 May
1923][1]
AD. [24 075].
[1]Dated by the fact that the calculations are written on the back of Doc. 30.
[2]The first line is eq. (4) of Einstein 1923n (Doc. 52). Apparently, Einstein is reflecting on the
results of that paper for the case where expansion parameters σ and τ were explicitly introduced, as
in , etc.
[2]
gμν;α
1
2
--gμσ;σδα
-
ν

1
2
--gνσ;σδα
-
μ

1
2
--iμδα
-
ν
1
2
--iνδα
-
μ
+ + 0 =
Rμν
×
ασgμν
×
β----Tμν
τ2
σ
-
e) (
τ2
6σ2
-------- -iμiν
× ×
+–=
Γμν α
μν
α
¯ ¿
® ¾
­ ½
1
2
--gμνiα - . . +=
×
–βτfμν
1
6σ©
-----§
-
τ
∂iμ
∂xν
------- -
∂iν
∂xμ¹
--------·
=
βτ2
σ
--------§
Tμν
e) (
1
6σβ
----------iμiν¹·
× ×
+
©
–=
×
–fμν
1
6βσ©
----------¨
∂iμ
×
∂xν
--------
∂i×·
∂xμ¹
--------¸ν

§
=
gμν σgμν
×
=
fμν
τfμν×
=
sμν
τsμν×
=

τiμ×
=

gαμ
--------
×
τ
σ
--- = =
gμν σg×
μν
=
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