Tidal Deformability of Neutron Stars in Bumblebee Gravity: Probing Lorentz Symmetry Breaking with Gravitational Waves

We investigate the tidal properties of static neutron stars in the Neves–Gardim branch of bumblebee gravity, a vector–tensor theory in which a nonzero vacuum expectation value of the bumblebee field spontaneously breaks local Lorentz symmetry. The stellar background is determined from the full modified Tolman–Oppenheimer–Volkoff system, including the term containing $m^{\mathrm{\prime }\mathrm{\prime }}(r)$. For a differentiable barotropic equation of state, this system is recast into an algebraically equivalent first-order form without discarding any bumblebee-dependent contribution. Because a complete coupled derivation of static even-parity metric and bumblebee-field perturbations is not presently available for this stellar branch, the tidal sector is treated through an explicit effective metric-deformation prescription: the Hinderer fluid perturbation equation is evaluated on the modified bumblebee background, and the standard surface matching relation is retained as part of the same prescription. We compute the quadrupolar tidal Love number $k_2$ and the dimensionless tidal deformability $\mathrm{\Lambda }=(2\mathrm{/}3)k_2{\mathcal{C}}^{-5}$ for the BSk20, BSk21, DD2, and MS1 equations of state over $\mathrm{\ell }\in [-0.4,+1.0]$. The general-relativistic limit is recovered at $\mathrm{\ell }=0$ to within $0.2\mathrm{\%}$ in the benchmark calculations. Within the adopted effective prescription, comparison with the GW170817 binary tidal-deformability bound $\tilde{\mathrm{\Lambda }}\le 720$ yields the EOS-dependent limiting values ${\mathrm{\ell }}_{\max }=+0.25$ (BSk20), $+0.06$ (BSk21), $-0.09$ (DD2), and $-0.25$ (MS1). These tidal limits are conditional on the stated perturbative prescription and should be reassessed when the complete linearised vector–tensor problem becomes available.