How to calculate the attractive force in a gravitational field in General Relativity?

I believe that a gravitational field has energy, as Weinburg wrote in his textbook Gravitation and Cosmology, on page 171: "… … the gravitational field does carry energy and momentum." As long as two points in space have energies, they attract each other. Now consider two particles in the gravitational field of the Earth. I want to calculate the attractive force between these two particles, not due to their own mass or energy, but due to the gravitational field of the Earth. Following is what I have done.

First, I found the stress-energy tensor of the gravitational field, on page 165 of Weinburg’s book:
begin{equation}
t_{mu k} equiv frac{1}{8pi G} [R_{mu k} – frac{1}{2} g_{mu k} {R^{lambda}}_{lambda} – {R^{(1)}}_{mu k} + frac{1}{2}eta_{mu k}{R^{(1)lambda}}_{lambda}] tag{1}
end{equation}
where $R_{mu k}$ is Ricci tensor;
begin{equation}
{R^{(1)}}_{mu k} equiv frac{1}{2}(frac{partial^{2} {h^{lambda}}_{lambda}}{partial x^{mu}partial x^{k}} – frac{partial^{2} {h^{lambda}}_{mu}}{partial x^{mu}partial x^{k}} – frac{partial^{2} {h^{lambda}}_{k}}{partial x^{lambda}partial x^{mu}} + frac{partial^{2} h_{mu k}}{partial x^{lambda}partial x_{lambda}}) tag{2}
end{equation}
is the part of the Ricci tensor linear in $h_{munu}$, and
begin{equation}
h_{munu} = g_{munu} – eta_{munu}
end{equation}
is the difference between the metric of the curved space and Minkowski metric.

Next, on page 36 in Zee’s textbook Quantum Field Theory in a Nutshell, I found the interaction between two lumps of stress energy:
begin{equation}
W(T) = -frac{1}{2} int frac{d^{4}k}{(2pi)^{4}} T^{munu}(k)^{*} frac{(G_{mulambda}G_{nusigma} + G_{musigma}G_{nulambda}) – frac{2}{3} G_{munu}G_{lambdasigma}}{k^{2} – m^{2} +iepsilon}T^{lambdasigma}(k) tag{3}
end{equation}
where
begin{equation}
frac{(G_{mulambda}G_{nusigma} + G_{musigma}G_{nulambda}) – frac{2}{3} G_{munu}G_{lambdasigma}}{k^{2} – m^{2} +iepsilon}
end{equation}
is the propagator for a massive spin-2 particle.
As stated in Zee’s book, from the conservation of energy and momentum $partial_{mu}T^{munu}(x) = 0$ and hence
$k_{mu}T^{munu}(k) = 0$, we can replace $G_{munu}$ in (3) by $g_{munu}$, which can be further approxmiated by $eta_{munu}$ for the gravitational field of the Earth. Look at the interaction between two lumps of energy density $T^{00}$, we have from (3) that
begin{equation}
W(T) = -frac{1}{2} int frac{d^{4}k}{(2pi)^{4}} T^{00}(k)^{*} frac{1 + 1 – frac{2}{3}}{k^{2} – m^{2} +iepsilon}T^{00}(k) tag{4}
end{equation}

Applying (4) to my problem, i.e., calculating the attraction between two particles in the gravitational field of the Earth, $T^{00}(k)$ should be the energy density of the gravitational field of the Earth at the positions of these two particles. This energy density is given by (1), which is a complicated function of the metric and has nothing to do with $k$, the momentum of the propagating spin-2 particle (graviton). So, looking at (4), the integral seems divergent. I am stuck. How should I do the calculation?