Radial oscillations and stability of compact stars in Eddington-inspired Born-Infeld gravity

We study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired Born-Infeld gravity recently proposed by Banados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter \kappa of the theory is also investigated. We find that the fundamental mode is insensitive to the value of \kappa, while higher order modes depend more strongly on \kappa.

💡 Research Summary

This paper investigates the structure and radial stability of compact stars—such as neutron stars—within the framework of Eddington‑inspired Born‑Infeld (EiBI) gravity, a modification of General Relativity (GR) introduced by Banados and Ferreira in 2010. The authors first reformulate the Tolman‑Oppenheimer‑Volkoff (TOV) equations to incorporate the EiBI action, which adds a nonlinear Born‑Infeld term characterized by a single coupling constant κ. When κ → 0 the theory reduces to GR, while non‑zero κ modifies the effective pressure and energy density felt by the fluid. Two representative equations of state (EOS) are employed: a simple polytropic model (P = K ρ^Γ) to explore a range of stiffnesses, and realistic nuclear‑physics EOS (SLy and APR) that reproduce observed neutron‑star properties. By solving the modified TOV equations for a grid of κ values (both positive and negative) the authors generate mass‑radius (M–R) curves. Positive κ yields stars with larger radii for a given mass (gravity is effectively weakened), whereas negative κ produces more compact configurations (gravity is strengthened). The location of the maximum‑mass configuration shifts appreciably with κ, providing a potential observational constraint because the existence of ≈2 M⊙ neutron stars limits the allowed κ range.

To assess dynamical stability, the paper develops a linear radial perturbation formalism. Starting from the Lagrangian displacement ξ(r), the authors derive a Sturm‑Liouville eigenvalue problem for the squared eigenfrequencies ω_n², imposing regularity at the centre (ξ ∝ r) and vanishing Lagrangian pressure perturbation at the surface. Numerical integration yields the fundamental mode (n = 0) and higher overtones (n ≥ 1) for each stellar model. The key findings are: (1) The fundamental mode’s ω_0² passes through zero precisely at the maximum‑mass point of the M–R curve, reproducing the classic GR stability criterion that the turning point marks the onset of instability. (2) The fundamental frequency is remarkably insensitive to κ, changing by less than a few percent across the explored κ range. (3) Higher‑order modes display a clear κ‑dependence: for κ > 0 the overtones shift to higher frequencies, while κ < 0 drives them lower. This behavior reflects the fact that overtones probe the detailed internal stratification and compressibility, which are directly altered by the EiBI modification.

The authors discuss the physical implications of these results. Since the basic stability condition remains unchanged, EiBI gravity does not introduce exotic instabilities in compact stars; rather, it subtly reshapes the stellar interior, leaving the overall mass‑radius relationship and the location of the stability limit largely intact. The κ‑sensitivity of overtones suggests that precise measurements of neutron‑star oscillation spectra—whether through gravitational‑wave asteroseismology or electromagnetic quasi‑periodic oscillations (QPOs) observed in magnetar flares—could serve as novel probes of the EiBI coupling. By comparing the theoretically predicted frequency shifts with future observations, one could place tighter bounds on κ than those obtained from purely static M–R measurements.

In conclusion, the paper provides a comprehensive framework for constructing equilibrium EiBI stars, performing radial perturbation analyses, and interpreting the resulting mode spectra. It confirms that the traditional GR stability paradigm survives the EiBI extension, while highlighting that higher‑order radial modes are promising diagnostics for testing this alternative theory of gravity in the strong‑field regime.