Collective scalarization or tachyonization: when averaging fails

TL;DR

This paper investigates when averaging over matter properties fails to predict scalarization in scalar-tensor gravity theories, showing collective effects can induce scalarization in composite bodies near the threshold, but not in dilute bodies.

Contribution

It demonstrates that collective effects can induce scalarization in composite bodies with constituents near the critical compactness, challenging the validity of simple averaging procedures.

Findings

Collective effects enable scalarization in bodies with constituents near the critical compactness.

Scalarization of dilute bodies requires a global compactness exceeding the critical threshold.

Averaging over local matter properties can fail to predict scalarization due to collective phenomena.

Abstract

Certain scalar-tensor theories of gravity provide negative-energy, tachyonic modes to a fundamental scalar inside matter, giving rise to non-perturbative phenomena around compact stars. Studies of this and other tachyonic instabilities always average over local matter properties. We use elementary, flat space models to understand possible collective effects and the accuracy of the averaging procedure. In particular, we consider bodies made of elementary constituents which do not, in isolation, scalarize because their compactness ${\cal C}$ is too small, ${\cal C}\lesssim {\cal C}_{\rm crit}$. We show that when the individual constituents have compactness smaller but close to the threshold, one is able to scalarize composite bodies through collective effects, and the compactness of the composite body can be made arbitrarily small. On the other hand, our results suggest that when the fundamental building blocks have very low compactness, then scalarization of the composite body requires a global compactness ${\cal C}_{\rm global}\gtrsim {\cal C}_{\rm crit}$. Thus, our results rule out scalarization of dilute bodies via collective effects.