Black holes and causal structure in anti-de Sitter isometric spacetimes

Abstract

The observation that the 2+1 dimensional BTZ black hole can be obtained as a quotient space of anti-de Sitter space leads one to ask what causal behaviour other such quotient spaces can display. In this paper we answer this question in 2+1 and 3+1 dimensions when the identification group has one generator. Among other things we find that there does not exist any 3+1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unexpected properties. For example, it turns out to be non-static and to possess a non-trivial apparent horizon.

Rotating topological black holes

“…In this connection, one should use a kind of quasi-local formalism for black hole thermodynamics, along the lines of Brown et al [36] for asymptotically anti-de Sitter black holes. One may note, among other things, that J = 0 for the locally anti-de Sitter solution corresponding to η = 0, in agreement with Holst's and Peldan's theorem [10]. Physically, in this case Ω H = Ω ∞ and the horizon does not rotate relative to the stationary observers at infinity.…”

Anti-de Sitter space, squashed and stretched

“…(We make it brief, because it was fully spelt out elsewhere [8,11].) We will be especially interested in the Killing horizons that arise.…”

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

“…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 .…”