Understanding Photon Interactions: Source Gravitational Wells vs. External Fields:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

20th February, 2024

This additional description provided here enhances the paper titled, 'Distinguishing Photon Interactions: Source Well vs. External Fields' by providing a more detailed explanation of the principles discussed. It expands upon the concepts of energy expenditure, gravitational redshift, and momentum exchange in a clear and concise manner. Additionally, the inclusion of mathematical formulations further strengthens the paper by providing quantitative insights into the phenomena under investigation.

This study delves into the intricate interactions of photons within gravitational fields, discerning between encounters with source gravitational wells and external gravitational fields. When photons escape source gravitational wells, such as those of stars or black holes, they expend energy, leading to gravitational redshift. Conversely, when traversing external gravitational fields, photons maintain their inherent energy while experiencing bending paths due to momentum exchange. Through mathematical formulations, we elucidate these principles, offering insights into astrophysical dynamics and gravitational physics.

When a photon or wave escapes a gravitational well, such as the gravitational field of a massive object like a star or a black hole, it expends energy in the process. This energy expenditure, resulting from a change in energy ΔE, follows the Planck equation:

• ΔE = hΔf

It's crucial to note that:

a. This alteration in photon frequency (Δf) corresponds to a change in photon wavelength (1/Δλ), leading to a redshift of the photon wavelength.

b. The change in photon wavelength (1/Δλ) is directly proportional to the photon's distance from its source gravitational well. This distance remains constant throughout the photon's journey, even when traversing through the gravitational field of external massive bodies like planets or galaxies. However, instead of experiencing energy variations in strong gravitational fields, the photons maintain their inherent energy (E = Eg) through the equation (Eg = E + ΔE = E − ΔE), while undergoing gravitational redshift due to (ΔE = hΔf).

c. In addition to undergoing gravitational redshift, photons also experience redshift due to cosmic expansion, but this occurs only when they enter dark energy-dominated intergalactic space.

Through these mathematical formulations, we elucidate the principles governing photon interactions in source gravitational wells versus external gravitational fields, thereby enhancing our understanding of gravitational physics in astrophysical contexts.