Quantum Field Theory on compact stars near the Buchdahl limit

TL;DR

This paper investigates the effects of quantum fields on extremely compact stars near the Buchdahl limit, revealing that quantum stress tensor divergences can violate energy conditions and potentially alter classical stability bounds.

Contribution

It demonstrates that quantum field effects cause stress tensor divergences near the Buchdahl limit, challenging classical stability and energy condition assumptions for compact stars.

Findings

Quantum stress tensor diverges faster than classical source at the Buchdahl limit.

Violation of Null Energy Condition occurs near the inner light ring.

Quantum backreaction cannot be ignored as the star approaches the Buchdahl radius.

Abstract

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. Here, we consider the particularly simple model of a constant density star and we work in the probe approximation where the backreaction is ignored. We show that the trapping of modes inside the star 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 around the inner light ring. 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. The results are independent of the details of the interactions, but contain an ambiguity associated to the renormalization scheme.