From Navier-Stokes to Einstein

In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.

Section: Holographic Stress Tensorsmentioning

confidence: 87%

“…-7]. A different recent attempt [8][9][10] focuses on subregions of some Ricci-flat spacetime bounded by timelike hypersurfaces and reconstructs the metric of such a region from data belonging to a relativistic fluid describing the hydrodynamic regime of some QFT on the timelike boundary.…”

Section: Introductionmentioning

confidence: 99%

Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes

Costa

2012

“…According to the membrane paradigm [4], external observers will find that BH horizons behave like fluid membranes, endowed with a viscosity, conductivity, temperature, entropy, etc. Moreover, in certain circumstances there are formal mappings between solutions of general relativity and solutions of Navier-Stokes [5,6]. Fluids, however, lack strong uniqueness theorems and admit a rich structure of solutions.…”

Section: Jhep07(2014)045mentioning

confidence: 99%

Rings, ripples, and rotation: connecting black holes to black rings

Dias

Santos

Way

2014

105

Singly-spinning Myers-Perry black holes in d ≥ 6 spacetime dimensions are unstable for sufficiently large angular momentum. We numerically construct (in d = 6 and d = 7) two new stationary branches of lumpy (rippled) black hole solutions which bifurcate from the onset of this ultraspinning instability. We give evidence that one of these branches connects through a topology-changing merger to black ring solutions which we also construct numerically. The other branch approaches a solution with large curvature invariants. We are also able to compare the d = 7 ring solutions with results from finite-size corrections to the blackfold approach, finding excellent agreement. JHEP07(2014)045Introduction. As expressed by John Wheeler's statement, "Black holes have no hair" [1], black holes (BHs) in four spacetime dimensions are remarkably simple objects. The topology, rigidity, uniqueness, and no-hair theorems ensure that Kerr BHs are the only stationary, vacuum, and asymptotically flat solutions to general relativity, and that they are uniquely specified by their mass M and angular momentum J [2]. Because Kerr BHs are also linear mode stable [3], any stellar object undergoing gravitational collapse towards a BH is expected to settle to the Kerr solution.Yet, the uniqueness of the Kerr BH may seem surprising given the close connection between gravity and fluids. According to the membrane paradigm [4], external observers will find that BH horizons behave like fluid membranes, endowed with a viscosity, conductivity, temperature, entropy, etc. Moreover, in certain circumstances there are formal mappings between solutions of general relativity and solutions of Navier-Stokes [5,6]. Fluids, however, lack strong uniqueness theorems and admit a rich structure of solutions. Indeed, rotational instabilities appear in fluid droplets and non-spherical solutions develop [7]. In particular, a ring configuration is preferred for high spin. Therefore, it may be natural to suspect that BHs behave like fluid droplets and have a greater diversity of solutions. This is the emerging picture in d > 4 spacetime dimensions.In higher dimensions, gravity becomes weaker as it spreads out over extra dimensions. Horizons are therefore more flexible, creating new gravitational phenomena with no fourdimensional counterparts. For example, in d ≥ 5 black strings exist and suffer from the Gregory-Laflamme instability [8]. This instability leads to a fractal-like array of spherical BHs and cosmic censorship violation [9,10]. This behaviour is similar to the RayleighPlateau instability, where a fluid jet breaks into an array of spherical droplets [11].In addition, there are black rings with horizon topology S 1 × S d−3 . These have been constructed in closed analytic form in d = 5 [12] and numerically in d = 6 [13]. (The list of other BH horizon topologies that are allowed in d > 4 were discussed in [14]). In any d ≥ 5, black rings can be found perturbatively using the blackfold approach if the S 1 radius is much larger than the S d−3 radius [15]...

“…[28]. Here the effective gravitational dynamics of the D3-brane subject to Dirichlet boundary conditions at an appropriate cutoff surface was considered along the lines of ideas introduced in the paper(s) [29,30]. It was directly shown that the fluid/gravity correspondence and the hydrodynamic effective theory are obtained as the two (most interesting) extremes where the cutoff surface is taken to be located in the near-horizon throat region and at spatial infinity, respectively.…”

Section: Jhep04(2015)171mentioning

confidence: 99%

Probing the hydrodynamic limit of (super)gravity

Dato

Gath

Pedersen

2015

Abstract:We study the long-wavelength effective description of two general classes of charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes in ten and eleven dimensional supergravity. In particular, we consider gravitational brane solutions in a hydrodynamic derivative expansion (to first order) for arbitrary dilaton coupling and for general brane and co-dimension and determine their effective electro-fluid-dynamic descriptions by exacting the characterizing transport coefficients. We also investigate the stability properties of the corresponding hydrodynamic systems by analyzing their response to small long-wavelength perturbations. For branes carrying unsmeared charge, we find that in a certain regime of parameter space there exists a branch of stable charged configurations. This is in accordance with the expectation that D/NS/M-branes have stable configurations, except for the D5, D6, and NS5. In contrast, we find that Maxwell charged brane configurations are Gregory-Laflamme unstable independently of the charge and, in particular, verify that smeared configurations of D0-branes are unstable. Finally, we provide a modification to the mapping presented in arXiv:1211.2815 and utilize it to provide a non-trivial cross-check on a certain subset of our transport coefficients with the results of arXiv:1110.2320.