Radial perturbations of neutron stars in Scalar-Vector-Tensor (SVT)

TL;DR

This work studies neutron stars in a subclass of Scalar-Vector-Tensor (SVT) gravity by solving the generalized $TOV$ equations and analyzing radial perturbations. The authors focus on a simple, gauge-invariant SVT model with a single deviation parameter $\beta_4$ that couples the vector and scalar sectors, recovering GR as $\beta_4\to0$. They compute static neutron-star profiles for four realistic equations of state and show that nonzero $\beta_4$ can increase the maximum mass while modestly reducing the radius, indicating enhanced internal pressure support from the scalar-vector interaction. The radial perturbation analysis yields two decoupled degrees of freedom, with matter perturbations described by a Sturm–Liouville problem and scalar perturbations by a scalar quasinormal-mode equation, revealing shifts in mode frequencies and damping times relative to GR, dependent on $\beta_4$ and the equation of state. These results provide potential observational signatures of SVT gravity in strong-field regimes and motivate exploring broader SVT sectors and additional perturbation channels in future work.

Abstract

In this paper, we investigate the equilibrium configurations and the radial perturbations of neutron stars in a subclass of Scalar-Vector-Tensor (SVT) theories. By solving the generalised Tolman-Oppenheimer-Volkoff equations in SVT theories for several values of the modified gravity parameter, we examine the impact of the spontaneous scalarization of charged neutron star (NSs), which arises from the coupling of the scalar field to the electromagnetic tensor and double-dual Reimann tensor, $L^{μναβ}F_{μν}F_{αβ}$. Then we extend our study by deriving the action at quadratic order in linear perturbations of radial type and computing scalar quasinormal modes (QNMs)as well as the normal modes (NMs) showing the coincidence of stability and maximum mass points in generlar relativity (GR) is still present in this modified theory.

Figures (5)

• Figure 1: Mass-radius ($M$-$R$, left panel) and mass-central energy density ($M$-$\rho_c$, right panel) relations for various values of the coupling parameter $\beta_4$. The curves correspond to $\beta_4 = 0$ (solid lines), $\beta_4 = -0.0033$ (dashed lines), $\beta_4 = -0.0046$ (dot-dashed lines), and $\beta_4 = -0.0053$ (dotted lines). Four different equations of state, distinguished by color, are considered: FPS (purple), SLy (blue), BSk20 (green), and BSk22 (red).
• Figure 2: The first four normalized Lagrangian perturbations of the pressure $\Delta P/P(0)$ as a function of the radial coordinate for $\beta_4=-0.00333$. The numerical solutions satisfy the boundary condition \ref{['con1']} and \ref{['con2']} in the case of a neutron star with SLy EoS and central density $\rho_c=10\rho_0$.
• Figure 3: Squared frequency of the fundamental oscillation mode versus compactness, for the beyond-GR parameters $\beta_4=-0.00333$ (dashed lines), $\beta_4=-0.00467$ (dotdashed lines) and $\beta_4=-0.00533$ (dotted lines), together with the GR ($\beta_4=0$) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22.
• Figure 4: oscillation frequency as function of compactness, for the beyond-GR parameters $\beta_4=-0.00333$ (dashed lines), $\beta_4=-0.00467$ (dotdashed lines) and $\beta_4=-0.00533$ (dotted lines), together with the GR ($\beta_4=0$) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22.
• Figure 5: Imaginary part of $\omega$ ($\omega_I$) as function of compactness, for the beyond-GR parameters $\beta_4=-0.00333$ (dashed lines), $\beta_4=-0.00467$ (dotdashed lines) and $\beta_4=-0.00533$ (dotted lines), together with the GR ($\beta_4=0$) results (black lines). Four distinct equations of state are considered: FPS , SLy , BSk20 and BSk22.