Galileons and strong gravity

TL;DR

This paper investigates how cubic Galileon models with the Vainshtein mechanism suppress deviations from General Relativity in stars, showing that higher density stars exhibit minimal deviations, and scalar fields vanish beyond a critical density.

Contribution

It develops an approximation scheme for solutions inside the Vainshtein radius and demonstrates suppression of deviations from GR in rotating and relativistic stars within Galileon models.

Findings

Deviations from GR are suppressed by the Vainshtein mechanism even with rotation.

Higher density stars show more suppressed deviations from GR.

Scalar field solutions cease to exist above a critical density, near the maximum neutron star mass.

Abstract

In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find approximated solutions inside the Vainshtein radius, and show that deviations from General Relativity (GR), while considering rotation, are also suppressed by the Vainshtein mechanism. In a quadratic coupling model, in which the scalarisation effect can significantly enhance deviations from GR in normal scalar tensor gravity, the Galileon term successfully suppresses the large deviations away from GR. Moreover, using a realistic equation of state, we construct solutions for a relativistic star, and show that deviations from GR are more suppressed for higher density objects. However, we found that the scalar field solution ceases to exist above a critical density, which roughly corresponds to the maximum mass of a neutron star. This indicates that, for a compact object described by a polytropic equation of state, the configuration that would collapse into a black hole cannot support a non-trivial scalar field.