The Navier–Stokes equation and solution generating symmetries from holography

Berkeley, Joel; Berman, David S.

doi:10.1007/jhep04(2013)092

Cited by 16 publications

(26 citation statements)

References 56 publications

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“…Following the ideas of [40], we employ a similar reasoning to the flat metric discussed in chapter 3, which is done by solving the Killing equations perturbatively in the ε-expansion. We also found that Ehlers transformations may relate the Rindler and Taub spacetimes.…”

Section: Outline Of This Dissertationmentioning

confidence: 99%

“…For convenience, we are going to adopt the nomenclature used in [39,40]: we shall refer to the general transformations described by eq. (4.1) as the generalized Ehlers group, while their subset which specifically maps vacuum solutions into vacuum solutions shall be called the spacetime Ehlers group.…”

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

“…In a certain sense, we are going to build upon the work of [40], in that we will apply the Ehlers transformations in the context of the fluid/gravity duality. Their idea was to apply the Ehlers group to the Rindler metric at order ε 3 in the derivative expansion we described in the previous chapter.…”

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

“…That is, they imposed a Killing symmetry in a spacetime admitting a metric ansatz corresponding to the Navier-Stokes equation, applied the generalized Ehlers transformations preserving the ansatz and determined the induced transformation of the dual fluid's parameters, such as velocity, pressure and viscosity. In doing so, the authors of [40] applied some constraints on the new metrics as well as the isometries. An interesting result of [40] is that they found that the transformations they find are not part of the spacetime Ehlers group, but still produce solution-generating transformations for the dual fluid's fields.…”

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

“…One such example is known as the Ehlers group [35][36][37][38][39], which has first been applied in the context of fluid/gravity correspondence in 2012 [40]. On the other hand, there is a known symmetry group of solutions of the Navier-Stokes equations [41], which might also be of interest whenever someone mentions a duality between gravitational and fluid dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

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Tópicos da correspondência fluido gravidade em espaços planos

Soares¹

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Section: Outline Of This Dissertationmentioning

confidence: 99%

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

Section: Chapter 4 Solution-generating Symmetriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tópicos da correspondência fluido gravidade em espaços planos

Soares¹

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

Majhi

2019

J. High Energ. Phys.

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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 (JHEP 1207(JHEP , 146 (2012 [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 ǫ 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.

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Petrov type I condition and dual fluid dynamics

Cai

Yang

et al. 2013

J. High Energ. Phys.

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Recently Lysov and Strominger [arXiv:1104.5502] showed that imposing Petrov type I condition on a (p+1)-dimensional timelike hypersurface embedded in a (p+2)dimensional vacuum Einstein gravity reduces the degrees of freedom in the extrinsic curvature of the hypersurface to that of a fluid on the hypersurface, and that the leading-order Einstein constraint equations in terms of the mean curvature of the embedding give the incompressible Navier-Stokes equations of the dual fluid. In this paper we show that the non-relativistic fluid dual to vacuum Einstein gravity does not satisfy the Petrov type I condition at next order, unless additional constraint such as the irrotational condition is added. In addition, we show that this procedure can be inversed to derive the non-relativistic hydrodynamics with higher order corrections through imposing the Petrov type I condition, and that some second order transport coefficients can be extracted, but the dual "Petrov type I fluid" does not match the dual fluid constructed from the geometry of vacuum Einstein gravity in the nonrelativistic limit. We discuss the procedure both on the finite cutoff surface via the non-relativistic hydrodynamic expansion and on the highly accelerated surface via the near horizon expansion. *

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The Navier–Stokes equation and solution generating symmetries from holography

Cited by 16 publications

References 56 publications

Tópicos da correspondência fluido gravidade em espaços planos

Tópicos da correspondência fluido gravidade em espaços planos

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

Petrov type I condition and dual fluid dynamics

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