D O C U M E N T 3 0 M A Y 1 9 2 3 3 5

For the determinant , one obtains

where

Incl. the 2nd order terms, one hence obtains, if I now leave the factor out again

Maxwell’s energy tensor!

For you obtain the expression as before, where only takes the place of ;

I leave out the additional terms containing the current for now. If I then form out of

the equation : , I then obtain the law

Now I cannot avoid the following: (1) Maxwell’s energy tensor does indeed appear

here; but the equation only applies if it is weaker than the cosmological term .

And this appears to me to lie in the original assumption that always only an elec-

tromagnetic energy tensor of cosmological smallness can occur. (2) the sign is the

wrong one. According to the old theory it should read

thus

(Hence, either I get the cosmological term with the wrong sign or I get gravitational

repulsion instead of attraction.)

If in the symmetric part of one takes into account the additional terms con-

taining the current, then I find in addition to the usual Riemannian expression of

from the ’s the following additional terms— , means , where the

three-indices symbols are formed of course out of —:

γik ϕiαϕkα

–=

r riκ =

r g 1 ε2l … + + ( ), = l

1

2

--ϕikϕik.

- =

giα fα k g® δik

1

2

--lδik - ϕiαϕ kα –

© ¹

§ ·

+

¯ ¿

¾

½

=

° ° ® ° ° ¯

f

ik gϕik

=

Γkl α skl gkl

Rik gik = Rik sik – Riαsαk ⋅ =

Rik giαfαk g® δik

1

2

--lδik - ϕiαϕkα¹ –

©

§ ·

+

¯ ¿

¾.

½

= =

δik

Rik

1

2

--Rδik - – g{ δik Maxw.

Energ.tensor};

+ =

–R 4 g and =

Rik g( δik – Maxw.) + =

Rkl

Rkl skl γi

iα·

α

© ¹

§

sik