Momentum conservation in gravitational lensing?

Question

I have read this question:

Every time a photon changes direction, it requires something else to gain momentum in the opposite direction, whether a solar sail or a star bending light by gravity.

How is momentum conserved in diffraction?

Now I sincerely do believe that this answer is only for diffraction, and not gravitational lensing. In the case of diffraction, there is an actual interaction between the particles of the slit and the photons, that changes the photons' angle. In this case, the photon is able to exchange momentum with the particles of the slit.

Though, in the case of gravitational lensing, the photon is simply traveling along a null geodesic, a path in curved space. There is no need nor possibility to exchange momentum with the star that caused the lensing. But the reason I am in doubt is, that although, it is not possible for the photon to interact with the atoms of the star directly, it is possible for the photon to interact with the gravitational field of the star (to maybe exchange momentum).

So there are a few things that come to mind:

1. in the case of gravitational lensing, the photon moves along a null geodesic, and no need and no possibility to exchange momentum with the star directly

2. the photon is interacting with the star's gravitational field, and could exchange momenutum

So basically, I am asking whether the star moves (even if a tiny bit) towards the photon that passes by because of the (exchange of the) photon's momentum in the case of gravitational lensing.

Question:

1. Momentum conservation in gravitational lensing?

Answer 1

Whether it is a photon moving along the geodesic or our Moon in orbit around Earth does not matter: In both cases momentum conservation holds, and the star respective Earth does move.

Answer 2

When one talks of gravitational lensing and geodesics one is in the classical electromagnetic domain and in the gravitational model of General Relativity.

Momentum conservation belongs to the domain of Newtonian gravity. So modeling the light passing the star with Newtonian gravity and special relativity, so that the energy momentum of the classical EM wave can be treated as a mass, models the lensing observed, momentum conservation taken up by the star.

Individual photons are quantum entities. The classical EM is built up by a large number of photons in a field theoretical way, the geodesics they follow in the GR frame will be many. Unless gravity is quantized definitively the description will be open.

Geodesics are connected with energy and momentum conservation in a mathematical way, so even for single photons following a geodesic, it is the geometry that assures momentum conservation.