Non-linear Q-clouds around Kerr black holes

TL;DR

This paper demonstrates the existence of non-linear scalar field configurations, called Q-clouds, around Kerr black holes, which extend the known linear superradiant bound states and lead to new hairy black hole solutions.

Contribution

It introduces Q-clouds as non-linear bound states around Kerr black holes, expanding the understanding of scalar fields in black hole spacetimes beyond linear superradiant modes.

Findings

Q-clouds exist as non-linear bound states around Kerr black holes.

Q-clouds form a 2D parameter space, unlike linear clouds which are 1D.

Backreaction of Q-clouds leads to new hairy black hole solutions.

Abstract

Q-balls are regular extended `objects' that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces - existence lines - of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.