the metric is,The Schwarzschild Solution
To show that the Refractive metric is a
function of the mass and energy of objects in the environment we
consider the Refractive metric components in spherical polar
coordinates. It is assumed there is a central mass at the origin
of the coordinate system. In terms of the refractive index the metric is,
(44)
It is interpreted such that the refractive
index 
,
therefore the quantity 
can be expanded into a simple function of 
and 
, where 
is the distance
from the origin of the coordinates.
A wave function has a characteristic
wavelength, and its intrinsic dipole moment is proportional to
the distance between opposite amplitudes of the wave. Therefore
it is proportional to half the effective wavelength 
, or inversely
proportional to 
. The simplest function of the proper form can be reverse
engineered to fit the known solution,
(45)
In the case of a motionless central mass and a
negligible test particle the momentum is zero, so 
.
When referring to the polarizability of the
wave functions at the point P, this is actually in
the spirit of Mach’s principle. A wave function in
free space has no boundary, so there is non-zero probability for
any wave function to affect the polarizability at any point as a
function of the coordinates. This is consistent with the
Transactional Interpretation of Quantum Mechanics. The greater
the number of particles, the greater the probability of a
transaction. If the central object consists of N particles
of mass m, then this leads directly to the Schwarzschild
solution of the vacuum equation of General Relativity. Written in
the usual form as a function of 
, with 
, the total mass is given by the inverse
of the effective wavelength,
(46)
Note that in geometrical units mass always has units of inverse length. Therefore we have found the Schwarzschild metric can be expressed as a function of the polarizability in the region of the point P ,
(47)
Thus showing that the properties of mass, inertia and space-time curvature are just different aspects of the dispersion of probability waves.