Incompressible Fluids of the de Sitter Horizon and Beyond

Abstract

There are (at least) two surfaces of particular interest in eternal de Sitter space. One is the timelike hypersurface constituting the lab wall of a static patch observer and the other is the future boundary of global de Sitter space. We study both linear and non-linear deformations of four-dimensional de Sitter space which obey the Einstein equation. Our deformations leave the induced conformal metric and trace of the extrinsic curvature unchanged for a fixed hypersurface. This hypersurface is either timelike within the static patch or spacelike in the future diamond. We require the deformations to be regular at the future horizon of the static patch observer. For linearized perturbations in the future diamond, this corresponds to imposing incoming flux solely from the future horizon of a single static patch observer. When the slices are arbitrarily close to the cosmological horizon, the finite deformations are characterized by solutions to the incompressible Navier-Stokes equation for both spacelike and timelike hypersurfaces. We then study, at the level of linearized gravity, the change in the discrete dispersion relation as we push the timelike hypersurface toward the worldline of the static patch. Finally, we study the spectrum of linearized solutions as the spacelike slices are pushed to future infinity and relate our calculations to analogous ones in the context of massless topological black holes in AdS${}_4$.

27 pages, 8 figures

References in corpus (21)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Nonlinear Fluid Dynamics from Gravity
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• From Navier-Stokes To Einstein
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Towards a quantum theory of de Sitter space
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Quasinormal modes of D-dimensional de Sitter spacetime
• The holographic fluid dual to vacuum Einstein gravity
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• A de Sitter Farey Tail
• Higher Spin Realization of the dS/CFT Correspondence
• Addendum to Fast Scramblers
• Insightful D-branes
• Exact Gravitational Quasinormal Frequencies of Topological Black Holes
• Not One Bit of de Sitter Information
• Future Boundary Conditions in De Sitter Space
• Holography For a De Sitter-Esque Geometry
• Black Holes as Incompressible Fluids on the Sphere
• Some Thoughts on the Quantum Theory of de Sitter Space

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• De Sitter Horizons & Holographic Liquids
• Higher Spin de Sitter Holography from Functional Determinants
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• Towards a general fluid/gravity correspondence
• Holographic charged fluid dual to third order Lovelock gravity
• Interpolating geometries and the stretched dS${}_2$ horizon
• Entropy of causal diamond ensembles
• Petrov type I Condition and Dual Fluid Dynamics
• Flat space gravity at finite cutoff
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Petrov type I Spacetime and Dual Relativistic Fluids
• Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
• Effective metric in fluid-gravity duality through parallel transport: a proposal
• Moduli Stabilization and the Holographic RG for AdS and dS
• Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation
• Gravity dual of Navier-Stokes equation in a rotating frame through parallel transport
• A hydrodynamical description of gravitational waves
• Solution-generating transformations in duality-invariant theories and the fluid/gravity correspondence