### The fundamental gravitino and its physical dark world

## Chapter 10

THE EQUATION OF MOTION FOR THE FG ORIGINAL PARTICLE

Since the FG original particle possesses mass mF= 3.6 x 10-45 kg, we can use the Lagrangian of generalized Maxwell electromagnetic field to describe this mass. (10-1)

It is worth mentioning that the term in (10-1) violates U (1) gauge invariant. There exists an essential difference between Lagrangian (10-1) and that in the Maxwellian theory. Making use of the Euler- Lagrange equation (10-2)

We get the basic equation for the FG original particle ; (10-3)

Using the definition of field intensity

F�̦��� A�� - ∂��A��

A=(��,A)                                           (10-.4)

Under the Lorentz gauge, the equation of motion for FG original particle can be expressed in terms of electromagnetic potential A��.

(�� �C ��2) A  = 0

(�� �C ��2) ��  = 0                               (10-.5)

For static FG, equation reduces to (10-.6)

Therefore the Green function of FG equation, i.e. the responsive function of a point source G (r-r��) satisfies the following equation (10-7)

G = (10-8)

If the origin of the coordinate is put on the source point, the static potential can be rewritten (10-9)

Where g is a quantity, characterizing the strength of field intensity. The static field intensity is: (10-10)

Where (�� r) is a dimensionless quantity, and ��<1. Assuming FG original particle cannot drag the ��FG ether�� too strongly, this means g=0. In the following I will mainly put forward the gravitational effect of ��FG��.