Compact stars in scalar-tensor (ST) gravity have been extensively investigated, but relatively few studies have focused on highly relativistic neutron stars (NSs) with an extremely dense core region where the trace of the energy-momentum tensor reverses its sign. In this regime, we identify the origin of the phenomenon where multiple scalarized solutions exist for a fixed central density, arising from the oscillatory profile of the scalar field inside the star. This origin further indicates that the multibranch structure emerges for both negative and positive $\beta$, the quadratic-term coefficient in the effective coupling function between the scalar field and conventional matter in the Einstein frame. By comparing the Damour–Esposito-Farèse and Mendes-Ortiz models of the ST gravity, we demonstrate that their distinct scalarization behaviors stem from whether the effective coupling function is bounded. We also compute for scalarized NSs with a highly relativistic dense core in ST theories the moment of inertia and tidal deformability that are relevant to pulsar-timing and gravitational-wave experiments.

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• Alternative gravity theories
• Astrophysical studies of gravity
• Neutron stars & pulsars