D O C . 1 3 C O M M E N T O N G E N E R A L R E L A T I V I T Y 1 7

13. “Comment on My Paper ‘On the General Theory of

Relativity’”[1]

[Einstein 1923h]

Presented 12 April 1923

Published 15 May 1923

In: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische

Klasse. Sitzungsberichte (1923): 76–77.

In the following, the

formal[2]

essential aspects of the theory advanced in the cit-

ed paper are put forth once more in a clear overview, enriched by a new Hamilto-

nian form of expressing the theory, one that allows its relation to the general theory

of relativity in its original form to emerge particularly clearly.

One bases an affine connection in the space-time continuum according to the

formula

(1)

which is limited a priori only by the symmetry

condition[3]

.

From it follows the existence of the second-order Riemann tensor

(2)[4]

as well as the circumstance that the determinant has the character of the

square of a scalar density. From this follows the invariance of the fundamental law

of the theory

. (3)

In this case the ’s should be considered as being expressed by the Γ’s and should

be varied according to the Γ quantities. One thus obtains 40 equations that can be

solved for the quantities Γ. This yields

[p. 76]

Aμ

δ Γαβ

μ Aαdxβ

–=

Γαβ μ Γβα μ =

rkl

∂xα

∂

Γkl

α

– Γkβ

α Γlβ

α

∂xl

∂

Γkα

α

Γkl

α

Γαβ

β

– + + =

r rkl =

δ® –r rd

³

¯ ¿

¾

½

0 =

rkl