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

TL;DR

This paper introduces new causal boundary-based definitions of null infinity and black holes, extending classical concepts to more general spacetimes, and proves a key black hole trapping result under these new definitions.

Contribution

It proposes a novel framework for defining null infinity and black holes using causal boundaries, applicable to a wider class of spacetimes than traditional conformal boundary methods.

Findings

Classic black hole trapping result extended to new definitions

Generalized plane wave spacetimes often lack black hole regions

Null infinity can be well-behaved without conformal boundaries

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 well-defined. In particular, it is shown that (generalized) black hole regions do not exist in a large family of these spacetimes.