added pointer to the recent

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

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)

added a cartoon of AdS sliced by hyperbolic slices

]]>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

- B. Allen, A. Folacci, Gary Gibbons,
*Anti-de Sitter space at finite temperature*, Physics Letters B Volume 189, Issue 3, 7 May 1987, Pages 304-310 (doi:10.1016/0370-2693(87)91437-7)

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

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

From here (2.30)

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

(why no $d$-coordinate?)

From here

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

Woops. All fixed now.

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

]]>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 $(n-1, 2)$ signature, as at anti de Sitter group?

]]>Up to isometry, the

$\sum_{i = 1}^{d+1} (x^i)^2 - (x^{d+2})^2 = 0$anti de Sitter spacetimeof dimension $d + 1$ is the pseudo-Riemannian manifold whose underlying manifold is the submanifold of the Cartesian space $\mathbb{R}^{d+2}$ that solves the equation

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

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