[Richard777 (OP)]

Can the Schwarzschild metric be modified to represent frequency?
See reference attached.

[Richard777 (OP)]

A ratio of constructive interference (C) is:   
C = (f_t + f_R)/f_S 

A ratio of destructive interference (D) is:          
D = (f_t - f_R)/f_S 

The product of opposite ratios is unity: CD = 1

Giving the frequencies of space-time;
f_S² = f_t² - f_R² 
See attachment.

[Bored chemist]

Can the Schwarzschild metric be modified to represent frequency?

If so, is it helpful to do so?
You can probably interpretive dance to represent a frequency but I don't see why you would bother.

As far as I can tell, your PDF essentially says that a black hole has a radius (indeed, the "no hair" theorem says that's all it has.), and there is a frequency of light which has a wavelength equal to that radius.

This is trivially true, but doesn't seem useful.
The same could be said of , for example, sports arenas.

[Richard777 (OP)]

The benefit of a scalar frequency field occurs if there is an interaction between two particles.

The interaction results in a scalar force field. Frequency provides a link between the Schwarzschild metric and the Schrodinger energy equation. This is an interesting connection.

See attachment