A novel notion of null infinity for c-boundaries and generalized black holes

Abstract

We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime (M, g). These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general context: if the null infinity is regular (i.e. well behaved in a suitable sense) and (M, g) obeys the null convergence condition, then any closed trapped surface in (M, g) has to be inside the black hole region. As an illustration of this general construction, we apply it to the class of generalized plane waves, where the conformal null infinity is not always welldefined. In particular, it is shown that (generalized) black hole regions do not exist in a large family of these spacetimes.

The c-completion of Lorentzian metric spaces

“…A promising tool in the context of non-regular spaces is the causal boundary construction. Recall, for instance, the central role played by this construction to refine notions like the null infinite or the black hole in the regular case [8]. These definitions rely on the notion of completeness of geodesics, which can be translated (at least in the timelike case) to the non-regular context by using Lorentzian distance (see [19]).…”

Causal completions as Lorentzian pre-length spaces

“…Though elegant and simple at first sight, the construction of the so called causal boundary of a spacetime involves many subtleties, specially when trying to endow it with some additional structure, like a topology or causal relations (see [16,37] and references there in for an up to date account). Recently, significant results have been accomplished in this regard, most notably the introduction of a notion of black hole based on the causal boundary [12].…”

Hausdorff closed limits and the c -boundary II: null infinity and black holes

“…We also revisit in the present context the notion of future null infinity and black holes for c-boundaries, recently introduced by us in [3] with an eye towards developing some aspects of the theory of black holes within the c-boundary paradigm.…”

“…In sections 4 and 5 we revisit the notions of future null infinity and black hole, respectively, first introduced in [3]. In [3] we deliberately pursued maximum generality (indeed our results there apply to any strongly causal spacetime), but at the price of introducing some rather technical-looking definitions and results. For example, in [3] we deal with the so-called total c-completion.…”

“…In [3] we deliberately pursued maximum generality (indeed our results there apply to any strongly causal spacetime), but at the price of introducing some rather technical-looking definitions and results. For example, in [3] we deal with the so-called total c-completion. We are then forced to deal with the possible interactions between future and past sets, even in describing objects such the future null infinity.…”