The Penrose Inequality and the Fluid/Gravity Correspondence

Abstract

Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by some Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. The analogous inequality in the context of fluid dynamics can provide a valuable tool in the study of finite-time blowups in hydrodynamics. We derive the inequality for relativistic and nonrelativistic fluid flows in general dimension. We show that the inequality is always satisfied at the ideal fluid order. At the leading viscous order, the inequality may be violated by relativistic fluid flows, while it is always satisfied by nonrelativistic incompressible flows. The inequality may be violated at the next to leading viscous order by both relativistic and nonrelativistic flows.

18 pages, Revtex

References in corpus (17)

• A Stress Tensor for Anti-de Sitter Gravity
• Nonlinear Fluid Dynamics from Gravity
• Local Fluid Dynamical Entropy from Gravity
• Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
• Universal hydrodynamics of non-conformal branes
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity
• Nonlinear viscous hydrodynamics in various dimensions using AdS/CFT
• Present status of the Penrose inequality
• Gravitational Collapse and Cosmic Censorship
• The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
• Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
• Relativistic CFT Hydrodynamics from the Membrane Paradigm
• Black brane entropy and hydrodynamics: the boost-invariant case
• CFT Hydrodynamics: Symmetries, Exact Solutions and Gravity
• Blow Ups of Complex Solutions of the 3D-Navier-Stokes System
• Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence

Cited by in corpus (9)

• From Navier-Stokes To Einstein
• Turbulent flows for relativistic conformal fluids in 2+1 dimensions
• A Holographic Path to the Turbulent Side of Gravity
• Black Holes as Incompressible Fluids on the Sphere
• Penrose Inequality for Asymptotically AdS Spaces
• On the fractal dimension of turbulent black holes
• Turbulence, Gravity, and Multimessenger Asteroseismology
• Holographic Hydrodynamics and Applications to RHIC and LHC
• Kerr/Fluid Duality and Singularity of Solutions to the Fluid Equation