Self-consistent neutron stars in a class of massive vector-tensor gravity

TL;DR

This paper develops self-consistent neutron star models within Einstein-bumblebee gravity, a massive vector-tensor theory, demonstrating that such models are compatible with black hole solutions and observational constraints, thus broadening the theory's astrophysical applicability.

Contribution

It constructs neutron star solutions in massive vector-tensor gravity without the previous global potential vanishing assumption, ensuring consistency with black hole solutions and observations.

Findings

Neutron star configurations are possible without a globally vanishing vector potential.

The potential is only violated inside the strong-field interior and restored at spatial infinity.

The framework remains consistent with existing black hole solutions and observational constraints.

Abstract

Einstein-bumblebee gravity, as a class of massive non-minimally coupled vector-tensor theories, provides a useful framework for constraining Lorentz symmetry breaking through astrophysical observations, largely due to the existence of exact static and spherically symmetric black hole solutions. These solutions are typically obtained under the assumption that the vector-field potential vanishes everywhere once the vector field acquires a nonzero radial vacuum expectation value. However, imposing this assumption globally obstructs the construction of self-consistent compact-star solutions. In this work, we elucidate the origin of this inconsistency through a detailed analysis of the field equations and construct neutron-star configurations by abandoning the global vanishing-potential assumption. Crucially, we show that even without enforcing this condition everywhere, it is violated only in the strong-field interior region and is dynamically restored in the weak-field regime by asymptotic boundary conditions at spatial infinity. As a result, consistency with existing black-hole solutions and observational constraints is preserved. Our results establish massive vector-tensor gravity as a unified, natural, and self-consistent framework for compact objects, significantly extending its astrophysical viability beyond black holes and Solar System tests.