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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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

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