The Weak Field Approximation
  
From equation 3.6, the equation for the current densities is  
4.1
where   
The weak field approximation for the asymmetric metric tensor is  
4.2
where  is scalar field and   
To an approximation, equation 4.1 is   
4.3
Using equation 4.2 for the asymmetric metric, applying the gauge condition , and dividing by , equation 4.3 becomes  
4.4
 
With, equation 4.4 reduces to the classical wave-equation. In general equations 4.4 is for interactions mediated by massive bosons. For, equation 4.3 can be written in a more familiar form:  
where 
4.5
If   
 
Maxwells equations of Electro-magnetism are obtained. see reference [3]

For the special case , equation 3.2 is found to be, to an approximation

  
4.6
compare with Einsteins field equations: see reference [1] gives  The particular case for f=5,   
 
Is the energy-stress tensor of the Electro-magnetic field. see reference [3]