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.

事件视界和柯西视界是高度理想化的数学结构，并没有完全捕捉霍金辐射或质量膨胀的关键物理学。事实上，因为它们是目的论的，所以事件视界和柯西视界（在精确的技术意义上）都是物理上不可观察的。相比之下，通过检查零测地线的准局部行为，长寿命的视视距（或更普遍地说是长寿命的准局部视距）原则上是可观测的，并且“足够好”，可以务实地重新定义黑洞，并且“足够好”，可以产生霍金辐射。此外，现在也很清楚，长寿命的视视野（准局部视野）也“足够好”，可以产生大规模膨胀。这些观察表明，在试图将严格的数学定理外推到天体物理学领域时，应该小心一些，这些定理通常包含数学理想化，而这些理想化不一定与有限资源天文学家实际可以测量的内容相对应。