Why Does Einstein's Theory Predict an Odd Number of Gravitational Lens Images?

[Glenn]

Gravitational Lensing - question

An article published today at http://spaceflightnow.com/news/n0402/11lens/ stated that "Einstein's general theory of relativity predicts there should be an odd number of images, yet almost all observed lenses have only 2 or 4 known images."


How and Why does Einstein's General Relativity predict an odd number of images?

Thanks,
Glenn

 

[RMDumse]

A very simple explanation (perhaps too simple) would be, if there is enough gravitational field on one side of a body to bend light your way, then there will be enough gravitational field on the otherside to bend rays your way. So you will see one image on the central ray (unless the central ray is blocked by the gravitating body, but if that body is "transparent", like a galaxy which is mostly empty space rather than matter, then you will see the primary image). Additional images will appear as multiples of two on either side of the central image.

If you want to get into deeper detail, you could refer to: Burk, W.L. 1981, "Multiple gravitational imaging by distributed masses," Ap. J 244, L1.

 

[R0man]

According to Einstein's theory of general relativity, gravity is not a force between masses, but rather a curvature of space and time caused by the presence of massive objects. This curvature can cause light to bend as it passes through the gravitational field of a massive object, resulting in what is known as gravitational lensing.

In the case of strong gravitational lensing, where the gravitational field is particularly strong, multiple images of the same source can be produced. This is because the light from the source is bent and redirected in different directions, creating multiple paths for it to reach an observer.

Einstein's theory predicts that the number of images produced in strong gravitational lensing should be odd because of the way the light is bent and redirected. This is known as the "odd number theorem" and is a fundamental aspect of general relativity.

However, as mentioned in the article, most observed lenses only have 2 or 4 known images. This is because there are other factors that can affect the number of images produced, such as the shape and distribution of the mass causing the lensing. Additionally, some images may be too faint to be detected.

In summary, Einstein's general theory of relativity predicts an odd number of images in strong gravitational lensing, but there are other factors that can affect the actual number of observed images. Further research and observations are needed to fully understand the complexities of gravitational lensing.