Radial oscillations of neutron stars in Starobinsky gravity and its Gauss-Bonnet extension

TL;DR

This paper studies how modifications in Starobinsky gravity and its Gauss-Bonnet extension affect the radial oscillation stability of neutron stars, revealing significant differences from general relativity in stellar stability and exterior spacetime response.

Contribution

It provides the first detailed analysis of neutron star oscillations in Starobinsky and Gauss-Bonnet extended gravity theories, highlighting the impact of higher-derivative terms on stability.

Findings

Gravitational modifications influence stellar stability significantly.

Exterior spacetime responds dynamically to fluid oscillations, unlike in GR.

Stability transition occurs near maximum mass for high-density stars.

Abstract

Starobinsky gravity, as one of the simplest and best-behaved higher-curvature gravity theories, has been extensively studied in the context of neutron stars over the past few decades. In this work, we investigate the adiabatic radial oscillation stability of neutron stars within the framework of Starobinsky gravity. We find that gravitational modifications can significantly impact stellar stability. Specifically, the higher-derivative nature of the theory causes the exterior spacetime to dynamically respond to fluid oscillations, in contrast to general relativity where Birkhoff's theorem ensures a static exterior. For stellar models with low central densities, the fundamental frequency becomes nearly independent of the central density when the coupling constant is large. For stellar models with high central densities, the transition from stability to instability still approximately occurs near the maximum-mass configuration, similar to the case in general relativity. Our main analysis is conducted in the Jordan frame of the scalar-tensor gravity equivalent to Starobinsky gravity, and we explicitly verify consistency with results obtained in the Einstein frame. We further extend our study to a class of Gauss-Bonnet extensions of Starobinsky gravity.