We consider the one-dimensional nonlinear Dirac equation with cubic scalar self interaction, commonly known as the Gross--Neveu model. This equation admits solitary wave solutions of the form $\phi_{m,\omega}(x)e^{-i\omega t}$, where $m>0$ is the mass and $0<|\omega|<m$. In this talk, we discuss the spectral stability of non-relativistic solitary waves, namely the regime $\omega\in(m-\epsilon,m)$ for some sufficiently small $\epsilon>0$. We prove that, for $\epsilon$ sufficiently small, the essential spectrum of the linearized operator is given by $i\bigl((-\infty,-m+\omega)\cup(m-\omega,\infty)\bigr)$, while the point spectrum consists only of the symmetry-induced eigenvalues: a zero eigenvalue associated with translations and eigenvalues at $\pm 2\omega i$ arising from the underlying $SU(1,1)$ symmetry. We further establish limiting absorption principles at the thresholds of the essential spectrum, $\pm i(m-\omega)$, as well as at the embedded thresholds $\pm i(m+\omega)$. Our approach is based on analyzing the Schur complement of the linearized Dirac operator and relating it to a relatively compact perturbation of the linearized one-dimensional cubic nonlinear Schr\"odinger operator about its solitary wave. This is joint work with Nabile Boussa{\"\i}d, Andrew Comech, and Jonas Lührmann.