Buchdahl Limit and TOV Equations in Interacting Vacuum Scenarios

TL;DR

This paper extends the TOV equations to include interacting vacuum components, showing that such interactions can relax classical stability bounds and support ultra-compact stellar objects.

Contribution

It introduces a covariant energy exchange in TOV equations and demonstrates how vacuum interactions modify the Buchdahl limit, enabling stable ultra-compact configurations.

Findings

Interaction terms relax the pressure gradient near the Buchdahl limit.

Numerical results show finite central pressure with vacuum interactions.

Classical geometric bounds can be bypassed by vacuum coupling.

Abstract

We investigate the stability of ultra-compact stellar configurations in the context of an interacting vacuum component. By extending the Tolman-Oppenheimer-Volkoff equations to include a covariant energy exchange between the fluid and vacuum sectors, we examine how the classical Buchdahl stability limit is modified. We analyze two phenomenological interaction models: a coupling to the matter energy density gradient and a direct coupling to the spacetime curvature. Numerical integration reveals that while standard General Relativity predicts a central pressure divergence as the compactness approaches the Buchdahl threshold, the interaction term $Q_\nu$ relaxes the pressure gradient and maintains a finite, well-behaved central pressure for proper domains of the coupling parameter. These results demonstrate that an interacting vacuum provides a physical mechanism to bypass classical geometric bounds, potentially supporting ultra-compact objects in regimes previously considered singular.