D O C . 1 G R A V I T A T I O N A L W A V E S 9
1. “On Gravitational Waves”
[Einstein 1918a]
Submitted 31 January 1918
Published 21 February 1918
In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1918):
154–167.
The important question of how gravitational fields propagate was treated by me in
an academy paper one and a half years
ago.1
However, I have to return to the sub-
ject matter since my former presentation is not sufficiently transparent and, further-
more, is marred by a regrettable error in calculation.
As before, I limit myself to the case where the space-time continuum that is un-
der consideration deviates only very little from a “Galilean” one. In order to be able
to write for all indices
, (1)
we select, as is customary in the special theory of relativity, the time variable as
purely imaginary, i.e., we put
,
where denotes the “light time.” In (1) or depending upon
or , respectively. The are small quantities compared to 1, and rep-
resent the deviation of the continuum from one that is free of fields; under Lorentz
transformations, they form a tensor of rank two.
1
These Sitzungsber. (1916), pp. 688 ff.
[p. 154]
[1]
[2]
[3]
gμν –δμν γμν + =
x4 it =
t δμν 1 = δμν 0 =
μ v = μ v ≠ γμν