1 4 D O C . 1 G R A V I T A T I O N A L W A V E S
(3a)
has to be used and, furthermore, by expressing the , with the help of (6) by
means of . One gets, after a simple
rearrangement,4
From this it follows that we satisfy the energy theorem if we set
(9)
The easiest way to grasp the physical meaning of the results from the following
consideration. The are for the gravitational field what the are for matter.
But for incoherent, ponderable matter one has, under limitation to quantities of first
order,
, (10)
4
The error in my previous paper [mentioned at the beginning] was that I had used
on the right-hand side of (8) instead of . This error also necessitates a rewriting of §2
and §3 of said paper.
γμν γμν

1
2
-- - δμν∑γαα

α
γμν

1
2
-- -
δμνγ

= =
Tρσ
[12]
γρσ

∂γ′
∂xμ
------------ρσ
∂γ
ρσ
∂xμ
----------
∂tμσ
∂xσ
σ
∑----------

∂xσ
--------
1
4κ⎝
------⎜
∂γαβ

∂xμ
----------------------⎟
∂γαβ⎞

∂xσ


1
2
-- -
∂γ′
∂xμ
----------------
∂γ′
∂xσ

αβ
∑⎜



1

------δμσ⎜
∂γαβ⎞

∂xλ
-----------⎟



2
1
2
-- -
∂γ′
∂xλ
--------


2
λ
∑⎝
αβλ








.
σ

=
[13]{2}
[p. 158]
4κtμσ
∂γαβ

∂xμ
----------------------⎟
∂γαβ⎞

∂xσ


1
2
-- -
∂γ′
∂xμ
----------------
∂γ′
∂xσ

αβ
∑⎜



1
2
--δμσ⎜ -
∂γαβ⎞

∂xλ
-----------⎟



2
1
2
-- -
∂γ′
∂xλ
--------


2
λ
∑⎝
αβλ





.



=
tμσ
tμσ Tμσ
Tμσ T
μσ
ρ----------------
dxμ
ds
dxσ
ds
where
ds2
ν
–∑dxν2⎠
=


, = =
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