Black holes, Cauchy horizons, and mass inflation

Event horizons and Cauchy horizons are highly idealized mathematical constructions that do not fully capture the key physics of either Hawking radiation or mass inflation. Indeed, because they are teleological, both event horizons and Cauchy horizons are (in a precise technical sense) not physically observable. In contrast, by inspecting the quasi-local behaviour of null geodesics, long-lived apparent horizons (or more generally long-lived quasi-local horizons) are in principle physically observable, and are “good enough" for then pragmatically redefining a black hole, and “good enough” for generating Hawking radiation. Furthermore it is now also clear that long lived apparent horizons (quasi-local horizons) are also “good enough" for generating mass inflation. These observations suggest that one should be somewhat careful when trying to extrapolate rigorous mathematical theorems, which often embody mathematical idealizations that do not necessarily correspond to what a finite resource astronomer can actually measure, into the astrophysical realm.