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The beginning of the lecture notes read: Ingemar Bengtsson ANTI-DE SITTER SPACE Fall 1998 Anti-de Sitter space is the maximally symmetric solution of Einstein's equatons with an attractive cosmological constant included; in reality the cosmological constant is certainly not attractive, but it is possible to regard it merely as a kind of regularisation of the long-distance behaviour of gravity. The conformal boundary of asymptotically anti-de Sitter space differs dramatically from that of asymptotically flat spacetimes, and this feature is usually crucial whenever anti-de Sitter space appears in mathematical physics. Notable examples are Friedrich's treatment of isolated systems in GR, the BTZ black holes, and also various studies in supersymmetry and string theory.

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The beginning of the lecture notes read: Ingemar Bengtsson ANTI-DE SITTER SPACE Fall 1998 Anti-de Sitter space is the maximally symmetric solution of Einstein's equatons with an attractive cosmological constant included; in reality the cosmological constant is certainly not attractive, but it is possible to regard it merely as a kind of regularisation of the long-distance behaviour of gravity. The conformal boundary of asymptotically anti-de Sitter space differs dramatically from that of asymptotically flat spacetimes, and this feature is usually crucial whenever anti-de Sitter space appears in mathematical physics. Notable examples are Friedrich's treatment of isolated systems in GR, the BTZ black holes, and also various studies in supersymmetry and string theory.
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Robert McNees (mcnees@mastodon.social)'s status on Thursday, 01-Dec-2022 16:11:02 UTC Robert McNees
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Lobachevsky's hyperbolic geometry (also studied by János Bolyai) shows up throughout physics, especially in relativity.
The Poincaré models described above are relevant for the AdS/CFT correspondence, as they describe a patch of (Euclidean) anti de Sitter space.
If you are curious about the relationship between AdS and hyperbolic geometry, and you've got some math under your belt, I strongly recommend Ingemar Bengtsson's ~beautiful~ lectures on Anti de Sitter space.
http://3dhouse.se/ingemar/Kurs.pdf

In conversation Thursday, 01-Dec-2022 16:11:02 UTC from mastodon.social permalink