Exotic Encounters: Buchdahl's Conditions and Physical Black Holes
arXiv:2505.09189 · doi:10.1142/S0218271825440134
Abstract
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, non-monotonic energy profiles, and strong pressure anisotropies. Thus, the requirement of truly forming a horizon places physical black holes in a class of solutions that are more exotic than exotic compact objects.
11 pages, 1 table. Honorable Mention for the Gravity Research Foundation 2025 Awards for Essays on Gravitation. Comments welcome!
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