Buchdahl Limit and TOV Equations in Interacting Vacuum Scenarios
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 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.
Cite
@article{arxiv.2604.13011,
title = {Buchdahl Limit and TOV Equations in Interacting Vacuum Scenarios},
author = {Rodrigo Maier},
journal= {arXiv preprint arXiv:2604.13011},
year = {2026}
}