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

TL;DR

The paper demonstrates that neutron-star solutions can be constructed in a class of massive vector-tensor gravity by discarding a globally enforced vanishing-potential condition, which previously prevented self-consistent stellar configurations. It derives the slow-rotation, modified Tolman-Oppenheimer-Volkoff equations and analyzes exterior vacuum solutions, showing that asymptotic boundary conditions restore the potential constraint at infinity while allowing strong-field interior deviations. Using the SLy EOS, it shows that even tiny Lorentz-violating parameters can significantly modify the mass-radius and I–M relations, with the vector-field potential shaping these deviations, akin to massive scalar-tensor theories. The work preserves compatibility with black-hole solutions and Solar System tests and points to future studies on stellar stability, oscillations, and tidal properties to further constrain the theory.

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.

Figures (3)

• Figure 1: The plots illustrate the numerical solutions of the functions ($f, \phi^{-1/2}, \rho, \lambda', w/\Omega$) in massive vector-tensor gravity with the parameters $\alpha = 10^{-4} \alpha_\star$ (solid lines) and $\alpha = 10^{-2} \alpha_\star$ (dashed lines). The parameter $\ell$ is fixed to $\ell=10^{-10}$. The central density is set to $\rho_0 = 1.2 \times 10^{15} \textup{g/cm}^3$, and the SLy EOS is adopted.
• Figure 2: Mass-radius ($M$-$R$, left) and mass-central density ($M$-$\rho_0$, right) relations for neutron stars described by the SLy EOS in massive vector-tensor gravity. The parameter $\ell$ is fixed to $\ell = 10^{-10}$. Different line styles correspond to $\alpha = 10^{-4}\alpha_\star$ (solid), $\alpha = 10^{-2}\alpha_\star$ (dashed), and GR (dotted).
• Figure 3: Moment of inertia-mass ($I$–$M$) relations for neutron stars described by the SLy EOS in massive vector-tensor gravity. The parameter $\ell$ is fixed to $\ell = 10^{-10}$. Different line styles correspond to $\alpha = 10^{-4}\alpha_\star$ (solid), $\alpha = 10^{-2}\alpha_\star$ (dashed), and GR (dotted).