1244 



Formula (18) holds for each system of coordinates in which the 

 spherical sj-mnietry is faken into consideration, if only the time- 

 coordinate is chosen so that ƒ/,„ = 0. If we specialize the system 

 of coordinates by |)ntting /> = !, then (he expressions (11) and (12) 

 are valid outside liie hody and for n and iv we obtain 



2c /« e'\ /ft e 



^^i.=- , -cU-2- 



r \r r I \ r r 



ca 



9Jr=-, (19) 



r 



Because of the spherical symmetry we have, of course, for the 

 components of '^1 in the directions of the axes of coordinates in space 



^U= -^ -, T= 1,2, 3. . . . . . (19a) 



r r' 



Making up the divergency we obtain 



and formula (16) gives 



:S— ^ = 0, (20) 



u= \2:t. 



Outside the body the right-hand side is zero and therefore also 



tl -0 (r>/0 ....... (21) 



//' the, system of coordinates is chosen so that p ^ 1 '), the 

 (gravitation field has everywhere outsjde the body the density of 

 energy zero. This is also true when the body is electrically charged, 

 because for the electro-magnetic field the sum of the diagonal compo- 

 nents of the stress-energy-tensor is eqtial to zero (see the note on 

 p. 1087). 



Now we may ask whether the oilier stress-energy-components A/ for 

 the gravitation field are also equal to zero. This is suggested by 

 formula fl7) I, which gives 



2 C = 0. 



a. 



That really all t,/ are zero in systems of coordinates for which 

 J) = 1 is easily proved with the aid of formula (52) of Einstein, 

 Grundlage. The details will be left here aside.") 



1) Then we have also V^ —g = c as has been proved in § 1 



2) For a non-electric centre E. Schrödingee has meanwhile proved this too : E. 

 ScHRöDiNGER, Die Energiekomponenten des Gravilationsfeldes. Phys. Zeitschr. 19, 

 1918 p, 4. (Remark in the proof.) 



