The Einstein ring is a special case of the gravitational lensing effect. It occurs when light from a more distant light source, aligned with a massive celestial object (such as a galaxy or a black hole), is bent by the gravitational influence of this object, resulting in the light appearing as a perfect ring in the observer's field of view. This phenomenon is one of the predictions of the theory of relativity and was first theoretically expressed by Albert Einstein in 1936.

Physical Basis

Einstein rings are related to the perfectly symmetric case of the gravitational lensing phenomenon, which arises as a consequence of the general theory of relativity. If:

• The background light source (e.g., a distant quasar),
• The foreground massive object acting as a lens (e.g., a galaxy cluster),
• And the observer (e.g., a telescope on Earth) are almost perfectly aligned, the light from the background source is bent by the lensing object and appears as a circular ring in the observer's field of view. This ring is called an Einstein ring. This ring is, in fact, a lensed image of a single source.

^{Einstein Ring (Generated by Artificial Intelligence)}

Mathematical Description

The angular radius of the Einstein ring can be calculated based on the following factors:

$\theta_E = \sqrt{ \frac{4GM}{c^2} \cdot \frac{D_{LS}}{D_L D_S} }$

Where:

• θ_E: Angular radius of the Einstein ring
• G: Universal gravitational constant
• M: Mass of the lens
• c: Speed of light
• D_S, D_L, D_LS​: Distances between observer-source, observer-lens, and lens-source, respectively

This formula shows how the observed bending angle in gravitational lensing depends on physical parameters.

Observability and Applications

Einstein rings provide important information for astronomical observations. Specifically:

• The distribution of dark matter,
• Galaxy mass profiles,
• Cosmological distance scales,
• And parameters such as the expansion rate of the universe,

can be measured through a detailed analysis of these rings. Radio telescopes and space telescopes (especially the Hubble Space Telescope) have been able to observe Einstein rings with high resolution. Some rings may not be perfectly circular but fragmented or elliptical; this is due to imperfect alignment or irregularities in the lens mass.