Anti-de Sitter quotients: when are they black holes?

Abstract

We point out that the BTZ black holes, and their relatives, can be defined in a cleaner way than they originally were. The covering space can be taken to be anti-de Sitter space, period, while J splits up into components due to Misner singularities. Our definition permits us to choose between two conflicting claims concerning BTZ black holes in 3 + 1 dimensions.

Cosmic Evolution from Phase Transition of Three-Dimensional Flat Space

“…Given these differences to previous constructions, it would be interesting to generalize our results to four (or higher) dimensions. This could be feasible, since also 4-(or higher-) dimensional AdS allows the construction of BTZ-like quotients, see [27] for a careful analysis and references therein for the original literature.…”

Anti-de Sitter quotients, bubbles of nothing, and black holes

“…Although this is de Sitter space times a circle, the conformal properties are quite different from that of de Sitter space itself [10]. The Penrose diagrams of these spacetimes are given in Fig.…”

“…The conformal boundary is denoted J , and is itself a conformal copy of the Einstein universe in one dimension less. In 3 + 1 dimensions all possible spacetimes arising by performing identifications using one-parameter subgroups of SO (3,2) have been classified [8,10]. A black hole is obtained when the subgroup is generated by the Killing vector…”

“…The details are explained elsewhere [1,[8][9][10], but since it is an interesting black hole we will pause to understand it. Its global isometries are generated by anti-de Sitter Killing vectors commuting with J ZU .…”

“…Indeed, as a three dimensional manifold J is independent of m, and the discussion of the τ + r + π -π/2 0 Fig. 2 This is τ + as a function of r + ; these quantities are defined in the text anti-de Sitter case m = 0 can be taken over verbatim [10]. In particular there will be an event horizon bounding the region of spacetime that can be seen from J .…”