light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime
Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it will propagate and spread slightly in the $x$ and $y$ directions. But what happens if we take into account self-gravitational effects of light onto itself? will the radiation flux self-gravitate and eventually reconverge?
Light undoubtedly possesses energy and momentum, impacting a specific energy distribution and potentially influencing the warping of space-time. However, the described situation where a radiating flow within a flat, unchanging space attracts and refocuses due to its own gravitational pull, requires further examination. Theoretically speaking, light might undergo a minimal self-focusing effect due to its gravity (similar to a slight bending), however, this effect is incredibly weak and often overshadowed by other influences. This bending refers to the deflection of light by massive objects and it holds more significance than the light's own gravity and it leads to observable phenomena like ring-shaped light distortions and minute gravitational lensing. Therefore, in most scenarios, the spreading of the light wave, either through diffraction or the bending caused by massive objects, is far more impactful than any self-gravitational focusing, so, while light does influence the curvature of space-time, its own gravitational effects typically have negligible observable consequences.
I first considered this question when I was 8 years old. In the subsequent 32 years my self-arrived conclusion is this; Diffusion. A ray of light will diffuse via the usual suspects until it is absorbed by the universe. Even a ray traversing the entire universe will be scattered, deflected, and consumed/absorbed before it can re converge on itself gravitationally. If your postulation is that the only thing in that universe is the ray of light, then, as it travels it expands the universe as it goes, which could be an interesting consideration for the expanse of the universe accelerating as it contracts.
