Graviton Propagator and energy-momentum tensor

[Neitrino]

Dear PF,
I am a little bit confused could you pls help me ...

Suppose I a have a scatering or conversion of two particles via graviton propagator.
Graviton propagator couples with energy-momentum tensor of matter fields.

So can i assume that vertex to which graviton propagator is coupled is in fact energy-momentum tensor ?

Energy-momentum tensor is conserved and thus if i take graviton propagator in some general case where i have graviton momentum in numerator it should give me vanishing contribution.

But energy-momentum tensor (which I cast in this case as a vertxe +external lines) contains two different momentum: ingoing momentum p1 and ingoing momentum p2, so my propagator momentum will be q=p1+p2... so does it mean that when I express graviton momentum through p1+p2 and and couple it to a vertxe i will have identical zero...?

Thanks

 

[fzero]

There are terms in the graviton propagator that do not have factors of the momentum in the numerator. For example, in harmonic gauge

$$D_{\mu\nu,\rho\sigma} = \frac{1}{q^2} \left( \eta_{\mu\rho}\eta_{\nu\sigma} + \eta_{\mu\sigma}\eta_{\nu\rho} - \eta_{\mu\nu}\eta_{\sigma\rho} \right).$$

This expression leads to the Newtonian potential in the nonrelativistic limit, as outlined for example, in section 4 of http://arxiv.org/abs/gr-qc/9512024.