A Holographic Path to the Turbulent Side of Gravity

We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS) black brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short to long wavelength modes via a turbulent cascade within the metric perturbation. As long wavelength modes have slower decay, this lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions, and the possibility of predicting turbulence in more general gravitational scenarios.Comment: 24 pages, 10 figures; v2: references added, and several minor change

Nonlinear electrodynamics as a symmetric hyperbolic system

Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg

Triggering magnetar outbursts in 3D force-free simulations

In this letter, we present the first 3D force-free general relativity simulations of the magnetosphere dynamics related to the magnetar outburst/flare phenomenology. Starting from an initial dipole configuration, we adiabatically increase the helicity by twisting the footprints of a spot on the stellar surface and follow the succession of quasi-equilibrium states until a critical twist is reached. Twisting beyond that point triggers instabilities that results in the rapid expansion of magnetic field lines, followed by reconnection, as observed in previous axi-symmetric simulations. If the injection of magnetic helicity goes on, the process is recurrent, periodically releasing a similar amount of energy, of the order of a few % of the total magnetic energy. From our current distribution, we estimate the local temperature assuming that dissipation occurs mainly in the highly resistive outermost layer of the neutron star. We find that the temperature smoothly increases with injected twist, being larger for spots located in the tropical regions than in polar regions, and rather independent of their sizes. After the injection of helicity ceases, the magnetosphere relaxes to a new stable state, in which the persistent currents maintain the footprints area slightly hotter than before the onset of the instability.Comment: 6 pages, 5 figure

Magnetosphere of an orbiting neutron star

We conduct force-free simulations of a single neutron star undergoing orbital motion in flat spacetime, mimicking the trajectory of the star about the center of mass on a compact binary system. Our attention is focused on the kinetic energy being extracted from the orbit by the acceleration of the magnetic dipole moment of the neutron star and, particularly, on how this energy gets distributed within its surrounding magnetosphere. A detailed study of the resulting magnetospheric configurations in our setting is presented, incorporating as well the effects due to neutron star spin and the misalignment of the magnetic and orbital axes. We find many features resembling those of pulsar magnetospheres for the orbiting neutron star - even in the absence of spin-of particular interest being the development of a spiral current sheet that extends beyond the light cylinder. Then, we use recent advances in pulsar theory to estimate electromagnetic emissions produced at the reconnection regions of such current sheets.Fil: Carrasco, Federico León. Max Planck Institute For Gravitational Physics (albert Einstein Institute); AlemaniaFil: Shibata, Masaru. Yukawa Institute For Theoretical Physics; Japón. Max Planck Institute For Gravitational Physics (Albert Einstein Institute); Alemani