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Limits and special symmetries of extremal black holes
Helgi Freyr Runarsson
Limits of spacetimes are obtained through a coordinate dependent procedure and in particular, limits of black hole spacetimes yield limit spacetimes that are some variants of anti-de Sitter space. These limits are of use in string theory, and in particular in the adS/CFT correspondence. By defining null coordinates, we are able to derive these limits in a clearer fashion for the whole spacetime and analyzing these new coordinates and the limit spactimes, we see which region of the limit spacetimes is covered by these coordinates.
Conformal isometries are special symmetries of spacetimes where the light cone structure of the spacetime is conserved. The charged black hole in a cosmological background possesses a discrete conformal isometry for certain values of its parameters and we show that this conformal isometry extends throughout the whole spacetime and beyond.
The Killing vector fields of the spinning black hole give insight into how an observer can move in certain regions of the spacetime. In particular, the so called velocity of light surface tells us where an observer can no longer corotate with the black hole. For an extremal black hole, we find that this surface lies both inside and outside the horizon of the black hole.