Buzz Bloom said:
What would the tensor equation look like describing the result of the motion of a neutron when a photon with a very large amount of energy passes near by the neutron? How would this motion of the neutron compare with the motion if there was no photon passing by?
Perhaps I can simplify this. I apologize for using Wikipedia as a source of information.
Energy is [a] quantitative property. A photon is an elementary particle. Photons are massless. (They have energy.) Matter is any substance which has mass. (@PeterDonis makes clear that photons are radiation.) Consider a flat space which is empty of all matter and radiation except for a single photon. As the photon travels, what does the corresponding tensor tell us about the time changing shape of space as the photon travels along a straight line? I am guessing that when the photon is at the origin x=y=z=0 the space shape at that time moves with the photon, both forward and backward in time.
All of this looks to me like a confused way of asking the question: how does light gravitate?
Since you have very little experience with tensors, you should probably not even try to formulate the question more specifically. You should certainly not be trying to guess what the answer is, or in what terms the answer is going to be usefully phrased. Terms like "time changing shape of space" are
not useful terms.
Also, you should beware of using the concept of "photon" in a classical context, which is the relevant context for this forum. (If you want to ask questions about the quantum nature of light, those questions belong in the quantum physics forum.) In a classical context, the best concept for what you appear to be interested in is "light pulse" or "null worldline". Such a thing is
not a "photon" except in the most informal, colloquial sense.
With those caveats, the general answer to the question "how does light gravitate" is to look at electrovacuum solutions to the Einstein Field Equation, i.e., solutions in which the stress-energy tensor is purely that of a vacuum electromagnetic field. If you want to take "light" to mean specifically electromagnetic
radiation, instead of allowing any electromagnetic field, then you would look at the subset of electrovacuum solutions in which the electromagnetic field is a radiation field (as opposed to, say, a static Coulomb field, as in the Reissner-Nordstrom charged black hole solution), or what is called a "null electrovacuum" in this Wikipedia article:.
https://en.wikipedia.org/wiki/Electrovacuum_solution
To see how individual test objects (like your "neutron") are affected by the gravitation of light, you would look at timelike test particle geodesics in whatever null electrovacuum solution you are using as your model.
One further note: all of this is way beyond a "B" level thread, so if you are really interested in it, you should start a separate thread.