Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

Higgs–Field and Gravity 107
From the field equation (29) it follows for the non-trivial Higgs–field
ground–state, c.f. (10) and (11)
for which the Higgs–potential (26) is minimized simultaneously; its corresponding
ground–state value is zero and herewith the field equations
(28) for the metric are fulfilled identically with the Minkowski–metric as
the metrical ground–state. Insertion of (35) into the Dirac equation (30)
and into the Higgs–field gauge current (32) of the Yang–Mills equation
(31 yields the fermionic mass–matrix (19 and the matrix of the mass
square of the gauge–bosons (20). In the unitary gauge the Higgs–field
takes the form (15).
Insertion of (14) and (15) into (28) gives the field equation of gravitation:
with the trace
and the equation of motion
According to (38) the excited Higgs–field generates a gravitation like
potential force acting on the massive particles as in section 1.
Obviously the Newtonian gravitational constant is defined as in (23)
only after symmetry breaking by the ground–state value Simultaneously
there exists a variability of the gravitational constant described by