Measuring the properties of homogeneous turbulence in curved spacetimes

Abstract

Turbulence in curved spacetimes in general, and in the vicinity of black holes (BHs) in particular, represents a poorly understood phenomenon that is often analysed employing techniques developed for flat spacetimes. We here propose a novel approach to study turbulence in strong gravitational fields that is based on the computation of structure functions on generic manifolds and is thus applicable to arbitrary curved spacetimes. In particular, we introduce, for the first time, a formalism to compute the characteristic properties of turbulence, such as the second-order structure function or the power spectral density, in terms of proper lengths and volumes and not in terms of coordinate lengths and volumes, as customarily done. By applying the new approach to the turbulent rest-mass density field from simulations of magnetised disc accretion onto a Kerr BH, we inspect in a rigorous way turbulence in regions close to the event horizon, but also in the disc, the wind, and in the jet. We demonstrate that the new approach can capture the typical behavior of an inertial-range cascade and that differences up to $40-80\%$ emerge in the vicinity of the event horizon with respect to the standard flat-spacetime approach. While these differences become smaller at larger distances, our study highlights that special care needs to be paid when analysing turbulence in strongly curved spacetimes.

13 pages, 14 figures, 4 appendices, matches accepted version on MNRAS

References in corpus (20)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
• Magnetic Reconnection and Hot Spot Formation in Black Hole Accretion Disks
• General relativistic simulations of compact binary mergers as engines of short gamma-ray bursts
• Plasmoid formation in global GRMHD simulations and AGN flares
• Broadband Multi-wavelength Properties of M87 during the 2017 Event Horizon Telescope Campaign
• The Properties of Short gamma-ray burst Jets Triggered by neutron star mergers
• On the Distribution of Plasmoids In High-Lundquist-Number Magnetic Reconnection
• EM counterparts of recoiling black holes: general relativistic simulations of non-Keplerian discs
• Spectral and Intermittency Properties of Relativistic Turbulence
• Universality and intermittency in relativistic turbulent flows of a hot plasma
• Spinning black holes magnetically connected to a Keplerian disk -- Magnetosphere, reconnection sheet, particle acceleration and coronal heating
• Microphysical Plasma Relations from Special-relativistic Turbulence
• Common-envelope Dynamics of a Stellar-mass Black Hole: General Relativistic Simulations
• Multipoint Turbulence Analysis with Helioswarm
• Turbulence modelling in neutron star merger simulations
• Statistical closures from the Martin-Siggia and Rose approach to turbulence

Cited by in corpus (2)

• The Role of Inhomogeneities in the Turbulent Accretion of Black Holes
• FPIC: a new Particle-In-Cell code for stationary and axisymmetric black-hole spacetimes