Self-interacting scalar field distributions around Schwarzschild black holes

TL;DR

This paper investigates how self-interactions in massive scalar fields influence the distribution and longevity of long-lived configurations around Schwarzschild black holes, revealing that self-interactions slightly enlarge the cloud but have a minor effect on lifetime.

Contribution

It provides a numerical analysis of the impact of both attractive and repulsive self-interactions on scalar field distributions around black holes, extending previous non-interacting models.

Findings

Self-interactions can increase the size of scalar field clouds.

Self-interactions have a subdominant effect on the lifetime of configurations.

The spatial distribution of quasi-stationary states is larger with self-interactions.

Abstract

Long-lived configurations of massive scalar fields around black holes may form if the coupling between the mass of the scalar field and the mass of the black hole is very small. In this work we analyze the effect of self-interaction in the distribution of the long-lived cloud surrounding a static black hole. We consider both attractive and repulsive self-interactions. By solving numerically the Klein Gordon equation on a fixed background in the frequency domain, we find that the spatial distribution of quasi stationary states may be larger as compared to the non interacting case. We performed a time evolution to determine the effect of the self-interaction on the life time of the configurations our findings indicate that the contribution of the self-interaction is subdominant.