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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2011

    earlier today I had created a stub for anti de Sitter spacetime

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 13th 2016

    Presumably super anti de Sitter spacetime

    A supergeometric analog of de Sitter spacetime.

    is missing an ’anti’.

    Can you have plain ’super de Sitter’? If so, I guess that wants an entry.

    By the way, aren’t I supposed to get the impression from anti de Sitter spacetime of an (n1,2)(n-1, 2) signature, as at anti de Sitter group?

    Up to isometry, the anti de Sitter spacetime of dimension d+1d + 1 is the pseudo-Riemannian manifold whose underlying manifold is the submanifold of the Cartesian space d+2\mathbb{R}^{d+2} that solves the equation

    i=1 d+1(x i) 2(x d+2) 2=0 \sum_{i = 1}^{d+1} (x^i)^2 - (x^{d+2})^2 = 0
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 13th 2016

    Woops. All fixed now.

    Regarding super de Sitter: not in the usual sense, but see arXiv:1610.01566

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 15th 2016
    • (edited Dec 15th 2016)

    Is this right yet? Don’t we need two coordinates of negative sign in the signature?

    From here (2.30)

    x 0 2+ i=1 d1x i 2x d+1 2=R 2-x_0^2 + \sum_{i = 1}^{d-1} x^2_i - x^2_{d+1} = -R^2

    (why no dd-coordinate?)

    From here

    an n+1n + 1 dimensional flat spacetime with signature (n1,2)(n - 1, 2), i.e. the set of points (X 1,X 2,,X n+1)(X_1, X_2, \ldots , X_{n+1}) satisfying (X 1) 2+(X 2) 2++(X n1) 2(X n) 2(X n+1) 2=1(X_1)^2 + (X_2)^2 + \ldots + (X_{n-1})^2 - (X_n)^2 - (X_{n+1})^2 = -1.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 16th 2016

    I gave what I think is the right definition, and mentioned the more general case of (p,q)(p, q) signature.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 15th 2018

    added pointer:

    Discussion of thermal Wick rotation on global anti-de Sitter spacetime (which is already periodic in real time) to Euclidean field theory with periodic imaginary time is in

    diff, v23, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2019

    added a cartoon of AdS sliced by hyperbolic slices

    diff, v27, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2020

    added this pointer:

    • Jiri Podolsky, Ondrej Hruska, Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes, Phys. Rev. D 95, 124052 (2017) (arXiv:1703.01367)

    diff, v34, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 22nd 2021

    added pointer to the recent

    • Anjan A. Sen, Shahnawaz A. Adil, Somasri Sen, Do cosmological observations allow a negative Λ\Lambda? (arXiv:2112.10641)

    diff, v37, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 28th 2024
    • (edited Jun 28th 2024)

    have re-written and expanded a little the section on coordinate charts (here)

    (it’s still minimalistic, though, not even mentioning global charts yet)

    diff, v41, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 28th 2024

    have spelled out (here) Cartan connection and curvature tensors for AdS spacetime in Poincaré coordinates

    diff, v41, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJul 1st 2024
    • (edited Jul 1st 2024)

    added pointer to:

    diff, v42, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJul 1st 2024

    and to:

    diff, v42, current