Stability Analysis of Spherically Symmetric Star in Scalar-Tensor Theories of Gravity

TL;DR

This paper investigates the stability of spherically symmetric stars in scalar-tensor gravity theories using quasi-normal modes, constraining the coupling function to align with observational stability requirements.

Contribution

It provides a novel stability analysis linking scalar-tensor theory parameters with astrophysical observations, constraining the coupling function based on relativistic star stability.

Findings

Certain ranges of the coupling function's derivative lead to instability.

Stability constraints exclude specific parameter ranges incompatible with binary-pulsar observations.

Analysis of scalar gravitational waves from stellar collapse enhances understanding of scalarization phenomena.

Abstract

A stability analysis of a spherically symmetric star in scalar-tensor theories of gravity is given in terms of the frequencies of quasi-normal modes. The scalar-tensor theories have a scalar field which is related to gravitation. There is an arbitrary function, the so-called coupling function, which determines the strength of the coupling between the gravitational scalar field and matter. Instability is induced by the scalar field for some ranges of the value of the first derivative of the coupling function. This instability leads to significant discrepancies with the results of binary-pulsar-timing experiments and hence, by the stability analysis, we can exclude the ranges of the first derivative of the coupling function in which the instability sets in. In this article, the constraint on the first derivative of the coupling function from the stability of relativistic stars is found. Analysis in terms of the quasi-normal mode frequencies accounts for the parameter dependence of the wave form of the scalar gravitational waves emitted from the Oppenheimer-Snyder collapse. The spontaneous scalarization is also discussed.