Exotic Encounters: Buchdahl's Conditions and Physical Black Holes

TL;DR

The paper investigates physical black holes (ΦBHs) — light-trapping regions that form in finite time for distant observers — and asks what matter content could physically realize them while satisfying or violating Buchdahl’s limit. Using a spherically symmetric, asymptotically flat framework and the Misner–Sharp–Hernandez mass with $f = 1 - \frac{2M(t,r)}{r}$, the authors classify near-horizon solutions into two classes with $k=0$ or $k=1$ and show that a visible horizon mandates violations of the null energy condition (NEC) and substantial pressure anisotropy; the energy-momentum tensor naturally decomposes into a radially moving null dust plus an anisotropic fluid. Consequently, ΦBHs violate all four Buchdahl conditions, implying that horizon formation requires exotic matter beyond horizonless exotic compact objects (ECOs). The results suggest that horizons, if they exist, push black-hole scenarios into a regime potentially signaling quantum-gravity effects at horizon scales, and they highlight that observations will be decisive in distinguishing between horizon-based and horizonless exotic objects in the ABH landscape.

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.