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