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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for apart geodesic distance | Date |
---|---|

B Orbits as geodesics | Apr 7, 2018 |

I Multiple geodesics | Apr 4, 2018 |

I How can General Relativity explain the Moon drifting apart from Earth | Mar 3, 2018 |

If two galaxies can drift apart in twice the speed of light, how can a third do it? | Dec 22, 2012 |

Does time exist apart from matter? | Mar 30, 2009 |

**Physics Forums - The Fusion of Science and Community**