Baryon-conserving radial modes and instability in matter-supported scalar–Gauss–Bonnet neutron stars

This paper investigates the onset of linear radial instability in matter-supported scalar–Gauss–Bonnet neutron stars with conformal matter coupling, a massive scalar field, and a cubic derivative interaction. All four strong-coupling reference configurations studied admit a growing radial (monopole) mode despite positive local radial kinetic and gradient coefficients. Their negative eigenvalues correspond to linear growth times of approximately 26–85 μs. Starting from the same action for equilibrium and perturbations, we derive the constrained fluid–scalar quadratic action and identify the baryon-conserving displacement domain. The formulation retains the zero-frequency sector and incorporates a moving material surface and a decaying exterior scalar field. Under the stated asymptotic assumptions, an explicit static spherical charge yields the first-law relation at fixed couplings. For the adopted stellar surface behavior, nonconserving equilibrium tangents are excluded from the physical perturbation space by their divergent kinetic norm. Kernel matching and spectral calculations identify four conserving turns with numerically simple kernels and resolved changes in eigenvalue sign. On the two traced strong-coupling branches, the conserving turn precedes the central-density fold and the approach to local admissibility loss. Independent weak-form and transfer calculations, together with negative Rayleigh quotients of compactly supported trial perturbations, support the reported instability. Near spatial degeneration, the tracked eigenvalue reaches −0.04886 km⁻² at the last computed regular state. Compact interval bounds apply to explicitly reconstructed coefficients. Rigorous spectral bounds for the exact nonlinear stellar solutions and the limiting coupled operator at spatial degeneration remain open. The accompanying supplement provides the equation of state, representative stellar backgrounds, spectral and diagnostic data, numerical source code, and instructions for regenerating the figures and tables and repeating selected calculations.