﻿Einstein and Grossmanns Theory of Gravitation. 91 



Each of both tensors can be taken as a representation of the 

 gravitational field. 



Action of Gravitation on Matter. 



12. The tensor (T<r„) which is closely connected with the 

 stresses, momenta, and energy is a mixed tensor. 



Of course, when a gravitation field acts upon matter (let 

 us include an electromagnetic field in the term matter) it 

 cannot be expected that the laws of conservation of momentum 

 and energy will hold for matter in itself alone. Obviously 

 the gravitational field can impart energy and momentum to 



the material s}-stem. In fact, the form > - — T ff p does not 



V 0<c v 



vanish now. Einstein gives for the influence of gravitation 



on other phenomena the formula 



X~~ =lX^ Vf y^rr (3) 



We notice that the terms which on the rioht-hand side of 

 the equation determine to what extent a given field will 

 influence the physical phenomena, are precisely the com- 

 ponents of the tensor of stresses and energy. This was 

 alluded to in section 2. 



As soon as matter and gravitation field are considered 

 together, then of course the laws of conservation must be 

 fulfilled. The existence must be supposed of a tensor of 

 stresses, momenta, and energy in the gravitational field 

 itself. Its components will be functions of the potentials 

 ffnv or %"v an d their derivatives, and, when this tensor is 

 denoted by t av , we shall demand that the laws are expressed 

 by the equations 



Differential equations for the creation of a gravitational 

 field by matter. 



13. This demand, this application of the laws of conserva- 

 tion, has been a guide in investigating the form of the dif- 

 rerential equations by which the gravitational held is 

 determined. There must be ten of them, because we have 

 ten potentials. Of course they are to be expected to be 

 extensions of the known equation of Poisson: 



A</> = kp 3 



where p is the density of the attracting mas-, and <j> the 



