If so, the wave function must approximate Newton gravitational acceleration at significant distances from the associated object. The field strength should be finite at the center of the object. The wave amplitude should be related to the Schwarzschild radius.

The “Newton catastrophe” permits infinite acceleration at the center of a massive object. This error may be avoided if the gravitational wave is finite at the center.

Can a gravitational field associated with a massive object, may be represented as a wave function?

Reference;

__http://newstuff77.weebly.com__ 06 Gravitational Wave Function

Let's take a closer look at your PDF.

Section "The Space-time Segment;": You define a segment, but the equation gives a coordinate. Did you mean "coordinate" instead of "segment", or did you mean to use $$\Delta x$$ instead of $$x$$ (etc.)?

Section "Field Stength;": You define $$g_r$$ to be a function of $$r$$. This is (as far as I know) non-standard notation; the usual notation would be $$g(r)$$.

The derivation of $$g_0$$ is missing.

The explanation of why "mean field strength" is equal to $$.5 g_0$$ is missing. Also, I think that's incorrect; there are many many more locations where the field strength would be lower than that.

Section "The Wave Function;": A function is introduced, but an explanation of its significance and the derivation are missing.

Section "The Field Equation;": This section does not contain a field equation; only some arithmetics with field strengths.

Section "The Gravitational Graph;": Some disjointed statements, and no graph.

Section "Newton Acceleration;": A previous equation is given, and $$t$$ is set to zero. This is nonsense: $$t=0$$ is whatever time you want it to be; it's not physical. The rest of this section is thus nonsense.

Section "Reciprocal Forces;": A previous equation is given. Some more arithmetics follow, with a conclusion about reciprocal forces $$F_r$$ and $$F_R$$ which have not been defined. This result is thus meaningless.

Section "Conclusion;": As others have already pointed out, there is no such thing as a "Newton Catastrophe" in mainstream physics, so it is not clear why it needed to be avoided in the first place.