Neutron stars in scalar-tensor theories of gravity and catastrophe theory

TL;DR

This paper explores the stability and equilibrium configurations of neutron stars within scalar-tensor gravity theories, revealing how certain choices of coupling functions lead to discontinuous changes in stability via catastrophe theory.

Contribution

It introduces a novel application of catastrophe theory to analyze neutron star stability and the phenomenon of spontaneous scalarization in scalar-tensor theories.

Findings

Stable equilibrium solutions can change discontinuously with scalar field parameters.

Cusp and fold catastrophes explain the stability behavior of neutron stars.

Spontaneous scalarization is characterized as a cusp catastrophe.

Abstract

We investigate neutron stars in scalar-tensor theories. We examine their secular stability against spherically symmetric perturbations by use of a turning point method. For some choices of the coupling function contained in the theories, the number of the stable equilibrium solutions changes and the realized equilibrium may change discontinuously as the asymptotic value of the scalar field or total baryon number is changed continuously. The behaviour of the stable equilibrium solutions is explained by fold and cusp catastrophes. Whether the cusp catastrophe appears or not depends on the choices of the coupling function. These types of the catastrophes are structurally stable. Recently discovered spontaneous scalarization, which is non-perturbative strong-field phenomenon due to the presence of the gravitational scalar field, is well described in terms of the cusp catastrophe.