# A What apart from geodesic distance matters in a spacetime that has lost its maximal symmetry?

1. Dec 11, 2017

### highflyyer

The isometry group of the anti-de Sitter spacetime is $SO(d-1,2)$, which has a total of $\frac{1}{2}d(d+1)$ isometries.

For the three-dimensional anti-de Sitter spacetime, these are $6$ isometries. These isometries have corresponding Killing vectors, which in global coordinates, are given in equation (9.8) of http://www.hartmanhep.net/topics2015/9-ads3symmetries.pdf.

For an AdS$_3$ cylinder (in global coordinates) that is radially cut-off at a finite radius, the number of isometries would decrease to $2$ because only $2$ of the Killing vectors in equation (9.8) of http://www.hartmanhep.net/topics2015/9-ads3symmetries.pdf are independent of the radial coordinate.

Now, any physical quantity on a maximally symmetric spacetime is a function of the geodesic distance. How does this fact change for the radially-cut-off AdS$_3$ cylinder?

Last edited: Dec 11, 2017
2. Dec 16, 2017

### PF_Help_Bot

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