According to our current understanding of physics, photons, which are particles of light, do possess energy and momentum and are affected by gravity. This means that photons do have a gravitational field, although the effects of their gravitational interaction are typically very small due to their lack of mass.
In Einstein's general theory of relativity, gravity is described as the curvature of spacetime caused by the presence of mass and energy. Photons contribute to the energy content of a system, and their presence can influence the curvature of spacetime, leading to gravitational effects.
While photons do not have rest mass, they do carry energy and momentum proportional to their frequency (or equivalently, their wavelength). This energy-momentum content of photons can have gravitational interactions with other masses and energy sources.
However, it's important to note that the effects of gravity caused by photons are typically much weaker compared to objects with mass. This is because the energy-momentum of a photon is directly related to its frequency through Planck's constant, and the frequency of visible light is many orders of magnitude higher than the typical energy scales associated with macroscopic objects. As a result, the gravitational effects of photons are usually negligible in everyday scenarios.
Regarding the "shadow effect" you mentioned, the absence of a shadow effect produced by photons is not due to the absence of a gravitational field but rather because photons themselves do not have a significant interaction with the hypothetical ether you mentioned. The concept of ether has been largely abandoned in modern physics, and our understanding of the interaction of light and gravitational fields is based on the framework of general relativity.
In summary, while photons do not have rest mass, they do possess energy and momentum and therefore have a gravitational field. However, the gravitational effects of photons are typically negligible compared to objects with mass, and the absence of a shadow effect is not related to the absence of a gravitational field but rather the lack of significant interaction between photons and the hypothetical ether.