Turbulent Black Holes

We demonstrate that rapidly spinning black holes can display a new type of nonlinear parametric instability—which is triggered above a certain perturbation amplitude threshold—akin to the onset of turbulence, with possibly observable consequences. This instability transfers from higher temporal and azimuthal spatial frequencies to lower frequencies—a phenomenon reminiscent of the inverse cascade displayed by ($2+1$)-dimensional fluids. Our finding provides evidence for the onset of transitory turbulence in astrophysical black holes and predicts observable signatures in black hole binaries with high spins. Furthermore, it gives a gravitational description of this behavior which, through the fluid-gravity duality, can potentially shed new light on the remarkable phenomena of turbulence in fluids.

Figure 1

Snapshots of parametrically driven modes on a sphere of constant radius. We plot the dominant (2, 2) spin $s=-2$ spheroidal harmonic from a collective driving mode, plus the spin-0 ($l$, 1) spheroidal harmonics for all of the growing scalar modes. Initially $h_0(t=0)=(1/8)\sqrt{\epsilon }$, and $\epsilon =2\times 10^{-3}$ ($\mathrm{a}=0.998$). In this case, modes with $2\le l\le 6$ are resonantly excited, with the higher $l$ modes growing faster; the $l>6$ modes are not ZDMs for this $a$. At $t/M=0$, the scalar modes are seeded with equal amplitude 10% of the gravitational mode, and random phases. (a) Reference spin $s=-2$, (2, 2) spheroidal harmonic. (b) At time $t/M=0$, the seed modes are visible only where the gravitational mode is weak. (c) At time $t/M=16$, more angular structure has developed. (d) The harmonics at $t/M=32$ when the amplitude of the (6, 1) scalar mode is closest to the (2, 2) mode.

Figure 2

Growth of the scalar quasinormal mode amplitudes due to a (2, 2) perturbation, on a logarithmic scale, using the same parameters as in Fig. 1. After initial parametric growth, the driving of each mode turns off as $h_0(t)$ decays, after which the scalar mode decays at its standard exponential rate, which is larger for modes with larger $l$.