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”
Submitted 31 January 1918
Published 21 February 1918
In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1918):
The important question of how gravitational fields propagate was treated by me in
an academy paper one and a half years
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
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.
These Sitzungsber. (1916), pp. 688 ff.
gμν –δμν γμν + =
x4 it =
t δμν 1 = δμν 0 =
μ v = μ v ≠ γμν