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- Odd_number_theorem abstract "The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. It says that the number of multiple images produced by a bounded transparent lens must be odd. In fact, the gravitational lensing is a mapping from image plane to source plane . If we use direction cosines describing the bent light rays, we can write a vector field on plane . However, only in some specific directions , will the bent light rays reach the observer, i.e., the images only form where . Then we can directly apply the Poincaré–Hopf theorem . The index of sources and sinks is +1, and that of saddle points is −1. So the Euler characteristic equals the difference between the number of positive indices and the number of negative indices . For the far field case, there is only one image, i.e., . So the total number of images is , i.e., odd. The strict proof needs Uhlenbeck’s Morse theory of null geodesics.".
- Odd_number_theorem wikiPageExternalLink 1010.3416.
- Odd_number_theorem wikiPageExternalLink lrr-1998-12.
- Odd_number_theorem wikiPageID "9156022".
- Odd_number_theorem wikiPageRevisionID "544667764".
- Odd_number_theorem hasPhotoCollection Odd_number_theorem.
- Odd_number_theorem subject Category:Gravitational_lensing.
- Odd_number_theorem subject Category:Physics_theorems.
- Odd_number_theorem type Abstraction100002137.
- Odd_number_theorem type Communication100033020.
- Odd_number_theorem type Message106598915.
- Odd_number_theorem type PhysicsTheorems.
- Odd_number_theorem type Proposition106750804.
- Odd_number_theorem type Statement106722453.
- Odd_number_theorem type Theorem106752293.
- Odd_number_theorem comment "The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. It says that the number of multiple images produced by a bounded transparent lens must be odd. In fact, the gravitational lensing is a mapping from image plane to source plane . If we use direction cosines describing the bent light rays, we can write a vector field on plane .".
- Odd_number_theorem label "Odd number theorem".
- Odd_number_theorem label "Odd-Number-Theorem".
- Odd_number_theorem sameAs Odd-Number-Theorem.
- Odd_number_theorem sameAs m.027zmx4.
- Odd_number_theorem sameAs Q280116.
- Odd_number_theorem sameAs Q280116.
- Odd_number_theorem sameAs Odd_number_theorem.
- Odd_number_theorem wasDerivedFrom Odd_number_theorem?oldid=544667764.
- Odd_number_theorem isPrimaryTopicOf Odd_number_theorem.