Superradiant instabilities in astrophysical systems

TL;DR

The paper investigates time-domain evolution of linearized massive scalar and vector fields around Kerr black holes to understand superradiant instabilities and bound-state dynamics. It employs a 3+1 framework on horizon-penetrating Kerr-Schild backgrounds, using Gaussian and bound-state initial data, and extracts radiation via scalar multipoles and Newman-Penrose scalars. A key finding is the beating modulation arising from interference among long-lived bound modes, which helps explain discrepancies between time-domain evolutions and frequency-domain growth rates reported in earlier work. The results demonstrate a particularly strong Proca-field instability in rapidly spinning Kerr spacetimes, with implications for constraining boson masses through BH spin observations and motivating further nonlinear and astrophysical investigations.

Abstract

Light bosonic degrees of freedom have become a serious candidate for dark matter. The evolution of these fields around curved spacetimes is poorly understood but is expected to display interesting effects. In particular, the interaction of light bosonic fields with supermassive black holes, key players in most galaxies, could provide colourful examples of superradiance and nonlinear bosenova-like collapse. In turn, the observation of spinning black holes is expected to impose stringent bounds on the mass of putative massive bosonic fields in our universe. Our purpose here is to present a comprehensive study of the evolution of linearized massive scalar and vector fields in the vicinities of rotating black holes. For a certain boson field mass range, the field can become trapped in a potential barrier outside the horizon and transition to a bound state. Because there are a number of such quasi-bound states, the generic outcome is an amplitude modulated sinusoidal, or beating, signal. We believe that the appearance of such beatings has gone unnoticed in the past, and in fact mistaken for exponential growth. The amplitude modulation of the signal depends strongly on the relative excitation of the overtones, which in turn is strongly tied to the bound-state geography. For the first time we explore massive vector fields in generic BH background which are hard, if not impossible, to separate in the Kerr background. Our results show that spinning BHs are generically strongly unstable against massive vector fields.

Figures (13)

• Figure 1: Time evolution of a dipole ($l=1,m=0$) scalar Gaussian wave packet in Schwarzschild background. We clearly observe the main features of such a field: (i) a prompt response at early times followed by (ii) the quasi-normal mode ringdown and (iii) a late-time tail.
• Figure 2: Amplitude of the scalar field extracted at $r_{\rm ex}=10~M$ as function of time obtained from the evolution of a scalar field initialized as spherical shell with space dependent mass $\mu_S^2 = -10M^2/r^4$, around a non-rotating BH.
• Figure 3: Evolution of a Gaussian profile of a massless scalar field with width $w=2~M$ centered at $r_0=12~M$ around a Schwarzschild BH (left panel) and around a Kerr BH with $a/M = 0.99$ (right panel). We depict the $l=0$ (solid black line) and $l=m=1$ (red dashed line) multipoles.
• Figure 4: Left and center: Initial profile of $|\Psi_{11}|^2$ for a bound state $m=1$ dipole configuration with $M\mu_S=0.42$ in a Schwarzschild (left panel) and $a/M=0.99$ Kerr background (mid panel). Black solid lines represent the fundamental mode and red dashed lines the first overtone. Right: Relative change of the modulus of the $(1,1)$ mode extracted at $r_{\rm ex}=20~M$.
• Figure 5: Upper left: $l=m=1$ multipole of run sS_m001 extracted at $10M$. The solid (black) line refers to numerical data, the dashed (red) to an oscillatory tail fit. Upper right: Same for sS_m100, extracted at $r_{\rm ex}=20~M$ (black solid line) together with the tail fit (red dashed line, we omit the oscillatory term for clarity). Lower Panels: $l=m=0$ multipole of runs sS_m042 (left, extracted at $20M$) and sK_m042 (right, extracted at $25M$). The solid black lines refer to the numerical data while the red dashed lines denote the the fit to the envelope of the oscillatory late-time tail.