Matter around Kerr black holes in scalar-tensor theories: scalarization and superradiant instability

TL;DR

This paper investigates how matter near Kerr black holes in scalar-tensor theories can induce instabilities, leading to scalar hair formation or superradiant amplification, revealing new dynamical phenomena in modified gravity.

Contribution

It identifies and analyzes two distinct instability mechanisms—tachyonic and superradiant—in Kerr black holes influenced by matter, expanding understanding of black hole dynamics in scalar-tensor theories.

Findings

Existence of scalarization due to negative effective mass squared.

Superradiant instability with high amplification factors.

Resonant scattering effects exceeding 10^5 in amplification.

Abstract

In electrovacuum stationary, asymptotically flat black holes in scalar-tensor theories of gravity are described by the Kerr-Newman family of solutions, just as in general relativity. We show that there exist two mechanisms which can render Kerr black holes unstable when matter is present in the vicinity of the black hole, as this induces an effective mass for the scalar. The first mechanism is a tachyonic instability that appears when the effective mass squared is negative, triggering the development of scalar hair --- a black hole version of "spontaneous scalarization". The second instability is associated with superradiance and is present when the effective mass squared is positive and when the black hole spin exceeds a certain threshold. The second mechanism is also responsible for a resonant effect in the superradiant scattering of scalar waves, with amplification factors as large as 10^5 or more.