Scalar fields from nonlinear sigma models on black hole spacetimes

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.