Exotic encounters: Buchdahl’s conditions and physical black holes

Black holes are among the most well-known astrophysical objects, yet their physical realisation remains conceptually subtle. We analyse physical black holes — light-trapping regions that form in finite time as seen by a distant observer — and investigate the properties of the matter required to support them. Taking Buchdahl’s theorem as a benchmark, we show that these configurations necessarily violate at least two of its four original conditions, and the post-formation state violates them all. These violations are substantial: They include the null energy condition, nonmonotonic energy profiles, and strong pressure anisotropies. Thus, the requirement of truly forming horizon places physical black holes in a class of solutions that are more exotic than exotic compact objects.