Equation-of-state sensitivity of the neutron-star scalar charge

Determine whether the dimensionless scalar-charge parameter q=3Q_phi/(GM), equivalently the pressure-weighted Yukawa scalar charge Q_phi of a neutron star in quadratic f(R)=R+alpha R^2 gravity, is sensitive to the neutron-star equation of state.

Background

In quadratic f(R)=R+alpha R2 gravity, a neutron star sources the scalaron inside its matter distribution, producing an exterior Yukawa correction whose amplitude is determined by the pressure-weighted scalar charge Q_phi. The paper parameterizes this amplitude by q=3Q_phi/(GM), with q=1 corresponding to the pressureless point-mass benchmark and 0<q<1 describing a neutron star; an isolated black hole has q=0 because it carries no scalaron hair.

The unresolved issue is whether q varies meaningfully with the neutron-star equation of state or instead obeys a quasi-universal relation largely independent of the equation of state. Resolving this would determine whether the scalar-charge correction can provide a direct equation-of-state diagnostic or whether it yields a more universal prediction for neutron-star exteriors and lensing observables.

References

Whether q is sensitive to the equation of state at all remains open, since scalar charges in scalar-tensor gravity obey quasi-universal relations~\citep{YagiStepniczka2021}: a universal value would sharpen the prediction, a spread would tie it to mass-radius measurements such as those from NICER timing of PSR~J0740+6620~\citep{Raaijmakers2021}.

— Screened Scalar Hair and the Weak-Lensing Separation of Black Holes from Neutron Stars in Quadratic $f(R)$ Gravity  (2609.04419 - Kumaran et al., 3 Sep 2026) in Section 4, “Neutron star exterior”