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Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation

  • Shounak De
  • Bibhas Ranjan Majhi
Open Access
Regular Article - Theoretical Physics

Abstract

Over the past few decades, a host of theoretical evidence has surfaced that suggest a connection between theories of gravity and the Navier-Stokes (NS) equation of fluid dynamics. It emerges out that a theory of gravity can be treated as some kind of fluid on a particular surface. Motivated by the work carried out by Bredberg et al. [6], our paper focuses on including certain modes to the vacuum solution which are consistent with the so called hydrodynamic scaling and discuss the consequences, one of which appear in the form of Damour Navier Stokes (DNS) equation with the incompressibility condition. We also present an alternative route to the results by considering the metric as a perturbative expansion in the hydrodynamic scaling parameter ϵ and with a specific gauge choice, thus modifying the metric. It is observed that the inclusion of certain modes in the metric corresponds to the solution of Einstein’s equations in presence of a particular type of matter in the spacetime. This analysis reveals that gravity has both the NS and DNS description not only on a null surface, but also on a timelike surface. So far we are aware of, this analysis is the first attempt to illuminate the possibility of presenting the gravity dual of DNS equation on a timelike surface. In addition, an equivalence between the hydrodynamic expansion and the near-horizon expansion has also been studied in the present context.

Keywords

Classical Theories of Gravity Black Holes Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of Technology GuwahatiGuwahatiIndia

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