Antidesitter space

Antidesitter space is a maximally symmetric , simply connected , pseudo-Riemannian manifold of constant negative curvature . It can be considered a pseudo-Riemannian analogue. $n$ ${\ displaystyle n}$ $n$ -dimensional hyperbolic space . Named as opposed to de Sitter space , usually denoted $AdS_{n}$ ${\ displaystyle AdS_ {n}}$ $AdS_ {n}$

In the language of the general theory of relativity , the antidesitter space is the most symmetric solution of the Einstein equations in vacuum with a negative cosmological constant $\Lambda$ ${\ displaystyle \ Lambda}$ $\ Lambda$ . The metric of such a space:

ds^{2}={\frac {1}{y^{2}}}\left(dt^{2}-dy^{2}-\sum _{i}dx_{i}^{2}\right)

{\ displaystyle ds ^ {2} = {\ frac {1} {y ^ {2}}} \ left (dt ^ {2} -dy ^ {2} - \ sum _ {i} dx_ {i} ^ { 2} \ right)}

{\ displaystyle ds ^ {2} = {\ frac {1} {y ^ {2}}} \ left (dt ^ {2} -dy ^ {2} - \ sum _ {i} dx_ {i} ^ { 2} \ right)}

.

Antidesitter space is represented as a one-sheeted hyperboloid embedded in a multidimensional Minkowski space ^[1] .

Notes

↑ Angsachon Tosaporn. Elements of the special and general theory of relativity in R- space. - SPb .: SPBU, 2013

Links

Space-time of negative curvature. // Juan Maldacena. The illusion of gravity. - Elements (Reprint from the journal "In the World of Science" No. 2, 2006)
Lecture 8. The Friedman Universe. The space of (anti-) de Sitter // M.O. Katanaev, Doctor of Physics and Mathematics n . Special course “General Theory of Relativity and Geometric Theory of Defects” - M. Steklov Mathematical Institute, 2015

[1] Angsachon Tosaporn. Elements of the special and general theory of relativity in R- space. - SPb .: SPBU, 2013

Antidesitter space

Notes

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