Compact stars in Quantum Field Theory

Very compact stars seem to be forbidden in General Relativity. While Buchdahl's theorem sets an upper bound on compactness, further no-go results rely on the existence of two light rings, the inner of which has been associated to gravitational instabilities. However, little is known about the role of quantum fields in these strong gravity regimes. Working in the probe approximation where the backreaction is ignored, we show that the trapping of modes around the inner light ring leads the renormalized stress tensor of Conformal Field Theories to diverge faster than the classical source in the Buchdahl limit. This leads to the violation of the Null Energy Condition, as well as the isotropy assumption used in Buchdahl's theorem. The backreaction of quantum fields in this regime therefore cannot be ignored. This happens as the star's surface approaches the Buchdahl radius 9GM/4 rather than the Schwarzschild radius, with the quantum fields having support in a small region around the center, becoming negligible at the surface. These are generic quantum features and do not depend on the details of the interactions.