Talks by Stephen Green

 Lorenz-gauge reconstruction for Teukolsky solutions with sources in electromagnetism

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
Reconstructing a metric or vector potential that corresponds to a given solution to the Teukolsky equation is an important problem for self-force calculations. Traditional reconstruction algorithms do not work in the presence of sources, and they give rise to solutions in a radiation gauge. In the electromagnetic case, however, Dolan (2019) and Wardell and Kavanagh (2020) very recently showed how to reconstruct a vector potential in Lorenz gauge, which is more convenient for self-force. Their algorithm is based on a new Hertz-potential 2-form.

Turbulent gravity in asymptotically AdS spacetimes

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
Dynamics in asymptotically anti-de Sitter spacetimes with reflecting boundary conditions are characterized by reduced dissipation as compared to asymptotically flat spacetimes. Such spacetimes, thus, represent opportunities to study nonlinear gravitational interactions that would otherwise be quickly damped away. I will discuss two background spacetimes---large AdS black branes in d=4, and pure AdS---where small perturbations display turbulent behavior and energy cascades driven by nonlinear interactions.

Nonlinear backreaction in cosmology

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)

In this talk I discuss the effects of nonlinear backreaction of small scale density inhomogeneities in general relativistic cosmology. It has been proposed that in an inhomogeneous universe, nonlinear terms in the Einstein equation could, if properly averaged and taken into account, affect the large scale Friedmannian evolution of the universe. In particular, it was hoped that these terms might mimic a cosmological constant and eliminate the need for dark energy. After reviewing some of these approaches, and some of their flaws, I will describe a perturbative framework (developed with R.

Superradiant instabilities of asymptotically AdS black holes

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)

Asymptotically AdS spacetimes with reflecting boundary conditions represent a natural setting for studying superradiant instabilities of rotating or charged black holes. In the first part of this talk, I prove that all asymptotically AdS black holes with ergoregions in dimension d ≥ 4 are linearly unstable to gravitational perturbations. This proof uses the canonical energy method of Hollands and Wald in a WKB limit.

Holographic Path to the Turbulent Side of Gravity

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
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 antide 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.

holographic path to the turbulent side of gravity

  • Adam Brown Stanford University
  • Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
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.

Newtonian and Relativistic Cosmologies

Stephen Green Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case.