Scalar fields from nonlinear sigma models on black hole spacetimes

TL;DR

This paper investigates nonlinear sigma model scalar fields on black hole spacetimes, revealing how their interactions influence gravitational wave signals and suppress phenomena like bosenova emissions, with implications for UV completions of gravity.

Contribution

It provides the first detailed simulation of nonlinear sigma model scalar fields on black hole backgrounds, analyzing their dynamics and effects on gravitational waveforms.

Findings

SL(2,R) model acts as an attractive self-interacting field.

O(3) model exhibits repulsive behavior.

Nonlinearities suppress bosenova emissions.

Abstract

Scalar fields with non-trivial kinetic term derived from a nonlinear sigma model are motivated by UV completions of gravity such as string theory. We discuss the $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{O}(3)$ sigma models with interacting potentials and simulate their full nonlinear dynamics on black hole spacetimes. We study the properties of the field as a function of the curvature of the sigma model with respect to the free massive scalar case. In the accretion process, the $\mathrm{SL}(2,\mathbb{R})$ model behaves as a self-interacting field with attractive interaction, while the $\mathrm{O}(3)$ one exhibits a repulsive phenomenology. In the case of a binary black hole system, these models cause a positive or negative dephasing of the gravitational waveform, respectively, when compared to the non-interacting case and as long as the field's Compton wavelength is larger than the binary separation. We observe no bosenova emission, which suggests that nonlinearities tend to suppress this phenomenon. Our results highlight how the kinetic and potential terms are both relevant in determining the field dynamics.