On the definition of black holes: Bridging the gap between black holes and singularities

Abstract

A novel perspective on defining black holes designed to be more broadly applicable outside of asymptotically flat spacetimes, in the context of classical general relativity, is presented, discussed, and characterized. The construction formalizes the heuristic idea that black holes are the “past Cauchy development of the set of singularities”. As such, the formulation depends in a critical way on the identification of singularities, which has been treated in the literature through various boundary constructions. While many of the known boundary constructions (e.g.Schmidt’s b-boundary or Geroch’s g-boundary) could in principal be cited as underlying one’s notion of a black hole, well-known topological concerns leads us to take the perspective that Scott and Szekeres’ abstract boundary provides the most natural choice. The framework is utilized to put forward a general, non-IVP formulation of the Weak Cosmic Censorship Conjecture.