Turbulent Black Holes

Abstract

We show that rapidly-spinning black holes can display turbulent gravitational behavior which is mediated by a new type of parametric instability. This instability transfers energy from higher temporal and azimuthal spatial frequencies to lower frequencies-a phenomenon reminiscent of the inverse energy cascade displayed by 2 + 1-dimensional turbulent fluids. Our finding reveals a path towards gravitational turbulence for rapidly-spinning black holes, and provides the first evidence for gravitational turbulence in an asymptotically flat spacetime. Interestingly, this finding predicts observable gravitational wave signatures from such phenomena in black hole binaries with high spins and gives a gravitational description of turbulence relevant to the fluid-gravity duality.Black holes are fascinating objects. They play a fundamental role in a plethora of energetic phenomena in our universe, for example as the engines of active galactic nuclei, X-ray binaries, and possibly even as regulators of galactic structure. In addition, they have become central tools in the study of field theories through the framework of holography [1]. This includes attempts to understand superfluidity, superconductivity and quark-gluon plasmas obtained in energetic collisions (see e.g. [2][3][4]). One particularly exciting connection inspired by holography is the "fluid-gravity" duality, which indicates the dynamics of black holes in asymptotically anti-deSitter (AAdS) spacetimes in d + 1 dimensions can be mapped to the physics described by conformal fluids governed by viscous, relativistic hydrodynamics in d dimensions [5,6]. This opens the door to search for particular behavior known to exist on one side of the duality on the other. For instance, this duality has motivated studies showing that particular gravitational scenarios can become turbulent when their fluid counterparts have high Reynolds numbers [7][8][9]. Additionally, concepts in hydrydonamics, such as ensthropy, have geometric counterparts related to curvature quantities [7]. This duality can also shed light on poorly understood phenomena from a new perspective. Analyzing turbulence from an intrinsically gravitational point of view is thus an exciting prospect.In this work we develop a method to do precisely this and consider realistic, asymptotically flat black holes. Our analysis describes how gravitational turbulence is mediated by a parametric instability in the gravitational field -which does not require the "confining properties" of asymptotically AdS spacetimes-and motivates the definition of a gravitational Reynolds number. We first review general properties of turbulent flows, salient features of the fluid-gravity duality, and parametric instability.Hydrodynamic turbulence. Turbulence is a ubiquitous property of fluid flows with sufficiently high Reynolds number (Re ≡ ρ/ηvλ >> 1) [10,11]. Here v and λ refer to the typical velocity and wavelength of characteristic modes of the solution, and ρ, η the fluid density and viscosity. At high Re, nonlinear interactions prevail...

Black hole squeezers

“…Sun and Price [50] discussed in detail how to construct Leaver's contour by analytic continuation and restored a factor that is missing in [49]. Similar techniques were also used by Yang et al [51] to define the inner product of the radial function of the QNMs. In this paper, we follow the method of Leaver (taking into account the missing factor) to regularize the radial integral to obtain a finite result.…”

Gravitational waves from a plunge into a nearly extremal Kerr black hole

“…The analysis in [5] also did not study in detail the behavior of the quasi-normal modes of the ringdown phase. The monochromaticity found in [5] could potentially be broken by the parametric resonance first seen in [6], which could potentially alter the waveform through mode-coupling.…”

Turbulence of Weak Gravitational Waves in the Early Universe

“…Our theory is, however, not strictly limited to the very early Universe. For example, turbulent black holes are potentially another application: our scenario based on four-wave interactions can be the explanation of the inverse cascade observed recently in [27][28][29][30]. Finally, we point out that in our case, the dual cascade behavior is caused by the fact that the leading-order interaction is four wave.…”

“…A turbulence theory seems to be particularly relevant for GWs because they are nonlinear, and their dissipation is negligible. Recent works [27,28] explore some ideas on similar lines: they investigate numerically the turbulent nature of black holes, define a gravitational Reynolds number, and show that the system can display a nonlinear parametric instability with transfers reminiscent of an inverse cascade (see also Refs. [29,30]).…”