Exotic Encounters: Buchdahl's Conditions and Physical Black Holes

TL;DR

This paper investigates the physical conditions necessary for black hole formation, revealing that such configurations require violations of classical energy conditions and involve exotic matter properties, distinguishing them from standard models.

Contribution

It demonstrates that physical black holes must violate multiple Buchdahl's conditions, highlighting their exotic nature compared to traditional compact objects.

Findings

Violations of Buchdahl's conditions are necessary for physical black holes.

Post-formation states violate all original Buchdahl's conditions.

Physical black holes involve exotic matter with null energy condition violations.

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.