Massive scalar field instability in Kerr spacetime

TL;DR

This paper investigates super-radiant instabilities of fields around Kerr black holes using time-domain 2+1D Teukolsky evolution. It shows that mirrors, either artificial or provided by a massive scalar field, can trap and amplify waves, creating a black-hole bomb with unbounded growth. Growth-rate estimates indicate a slow but real instability for massive fields and highlight mode dependence, with stronger growth for the l=m=1 mode and weaker for higher multipoles, compared with some frequency-domain results. The work validates time-domain methods for studying black-hole bomb instabilities and motivates broader parameter exploration for potential astrophysical implications.

Abstract

We study the Klein-Gordon equation for a massive scalar field in Kerr spacetime in the time-domain. We demonstrate that under conditions of super-radiance, the scalar field becomes unstable and its amplitude grows without bound. We also estimate the growth rate of this instability.

Figures (5)

• Figure 1: Black hole bomb: Massless scalar field sampled at $r_{*} = -20M$ in Kerr spacetime with $a/M=0.9999$ surrounded by perfect mirrors. The field grows without bound upon successive reflections. All quantities in units of black hole mass, $M$.
• Figure 2: Black hole bomb: Electromagnetic field sampled at $r_{*} = -20M$ in Kerr spacetime with $a/M=0.9999$ surrounded by perfect mirrors. The field grows without bound upon successive reflections. All quantities in units of black hole mass, $M$.
• Figure 3: Instability: Massive scalar field ($\ell=m=1$) sampled at $r_{*} = 20M$ in Kerr spacetime with $a/M=0.9999$. The field grows without bound, demonstrating the existence of instability. All quantities in units of black hole mass, $M$.
• Figure 4: Massive scalar field ($\ell=m=1$) sampled at $r_{*} = 20M$ in Kerr spacetime with $a/M=0.9999$. Here the super-radiance condition is not satisfied. The field decays, demonstrating the absence of an instability. All quantities in units of black hole mass, $M$.
• Figure 5: Instability: Massive scalar field ($\ell=m=2$) sampled at $r_{*} = 20M$ in Kerr spacetime with $a/M=0.9999$. The field grows without bound, demonstrating the existence of instability. All quantities in units of black hole mass, $M$.