Why Does dS Space Have a (4+1) Signature?

[Jim]

I am simply trying to understand why dS space has a signature (4+1) ?
Good old familiar Minkowski space is of course, (3+1), crystal clear.

What is the role of the extra spatial dimension in dS ? Why should the manifold be 5-D ?

 

[George Jones]

I am simply trying to understand why dS space has a signature (4+1) ?
Good old familiar Minkowski space is of course, (3+1), crystal clear.

What is the role of the extra spatial dimension in dS ? Why should the manifold be 5-D ?

de Sitter space does not have signature (4+1), it has signature (3+1). de Sitter space is particularly easy to visualize as a (3+1) 4-dimensional hypersurface in a 5-dimensional (4+1) Minkowski space. The hyperbolic hypersurface is (isomorphic to) de Sitter space, not the (4+1) Minkowski space.