Hyperbolic Cosmic Trousers: Topological Censorship and Multi-BTZ Black Hole Solutions in \(AdS_3\)

Abstract

We present a novel principle of strong topological censorship for the BTZ black hole solutions in \(AdS_3\). Specifically, we consider two initially separate threads. The first thread will ask if it is possible to construct stable dynamical solutions containing multiple BTZ black hole horizons within a single asymptotically \(AdS_3\) universe. The second thread will concern multi-BTZ black hole solutions with exterior asymptotically \(AdS_3\) regions which each contain only one BTZ black hole. In particular, we are interested in the topological censorship of such spacetimes. We then unite the two threads of inquiry, such that we attempt generalize to spacetimes with exterior \(AdS_3\) regions which contain more than one BTZ black hole horizon. We find that no such dynamical multi-black hole exterior region can exist, and that, instead, any attempts create a solution which contains such an exterior region will result in an emergent black hole horizon behind which, within some ``interior" region, the ``constituent" black hole horizons are now shielded from causal infinity \(\mathcal{J}\). This not only gives us a complete characterization of all possible locally \(AdS_3\) multi-BTZ black hole spacetimes, but also leads us finally to a stronger condition of topological censorship on \(AdS_3\) geometry itself. Specifically, this strong topological censorship will demand that the only non-trivial topology of a locally \(AdS_3\) spacetime which is allowed to be observable from \(\mathcal{J}\) is limited to that of a single BTZ black hole horizon.