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I need to find the geodesics of AdS_{3} spacetime. But my searches have given me nothing. Can anyone give a reference where they're calculated?
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The AdS3 space, also known as Anti-de Sitter space, is a three-dimensional space with constant negative curvature. It is a solution to Einstein's equations of general relativity and is used in various areas of theoretical physics, including string theory.
Geodesics in AdS3 are the shortest paths between two points in the AdS3 space. They are curves that follow the natural path of least resistance in the space, similar to a straight line in flat space.
There are several resources available for finding references on geodesics in AdS3. These include research papers, textbooks, and online resources such as lecture notes and videos. It is recommended to consult with a mentor or colleague in the field for guidance on the most relevant and reliable references.
Geodesics in AdS3 have numerous applications in theoretical physics, including in the study of black holes, quantum gravity, and holography. They also have implications for understanding the geometry and topology of the AdS3 space itself.
Yes, there are several challenges in understanding geodesics in AdS3. One of the main challenges is the highly non-linear nature of the equations involved, which makes it difficult to find exact solutions. Additionally, the concept of geodesics in curved spaces can be challenging to grasp for those unfamiliar with differential geometry.