The Petrov-like boundary condition at finite cutoff surface in Gravity/Fluid duality

Cutoff AdS/CFT duality and the quest for braneworld black holes

We present significant evidence in favour of the holographic conjecture that ``4D black holes localized on the brane found by solving the classical bulk equations in $AdS_5$ are quantum corrected black holes and not classical ones''. The crucial test is the calculation of the quantum correction to the Newtonian potential based on a numerical computation of $<T^a_b>$ in Schwarzschild spacetime for matter fields in the zero temperature Boulware vacuum state. For the case of the conformally invariant scalar field the leading order term is found to be $M/45πr^3$. This result is equivalent to the r…

Magnetohydrodynamics from gravity

Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the general framework for spacetime with matter field, and then derive the incompressible Navier-Stokes equations for black holes with electric charge and magnetic charge respectively. Especially, in the magnetic case, the standard magnetohydrodynamic equations will arise due to the existence of the background electromagnetic field on the hypersurface.

From Navier-Stokes to Maxwell via Einstein

We revisit the cutoff surface formulation of fluid-gravity duality in the context of the classical double copy. The spacetimes in this fluid-gravity duality are algebraically special, with Petrov type II when the spacetime is four dimensional. We find two special classes of fluids whose dual spacetimes exhibit higher algebraic speciality: constant vorticity flows have type D gravity duals, while potential flows map to type N spacetimes. Using the Weyl version of the classical double copy, we construct associated single-copy gauge fields for both cases, finding that constant vorticity fluids ma…

Fluid/gravity correspondence for massive gravity

In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gra…

Time evolving fluid from Vaidya spacetime

A time evolving fluid system is constructed on a timelike boundary hypersurface at finite cutoff in Vaidya spacetime. The approach used to construct the fluid equations is a direct extension of the ordinary Gravity/Fluid correspondence under the constrained fluctuation obeying Petrov type I conditions. The explicit relationships between the time dependent fluctuation modes and the fluid quantities such as density, velocity field and kinematic viscosity parameters are established, and the resulting fluid system is governed by a system of a sourced continuity equation and a compressible Navier-S…

弦论T-对偶启发的量子虫洞

Quantum-inspired wormholes from String T-Duality

该研究利用弦论T-对偶引入的紫外截断构建无奇异的球对称虫洞解，通过两种薄壳构造最小化零能量条件违反，提高虫洞的物理合理性与可穿越性。

Holographic duality for Ising CFT with boundary

We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix …

On the Magnetohydrodynamics/Gravity Correspondence

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. In this paper we extend this duality to a new magnetohydrodynamics/gravity correspondence, which translates solutions of the equations of magnetohydrodynamics (describing charged fluids) into geometries that satisfy the Einstein-Maxwell equations. We present an explicit example of this new correspondence in the context of flat Minkowski space. We show that a perturbative deformation of the Rindler wedge satisfies the Einstein-Maxwell equations provided …

Stationary Axisymmetric Solutions of the Einstein Equations with Rigidly Rotating Perfect Fluid and Nonlinear Charged Sources

A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state $3p + ε= constant$. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing a four- parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.

Compressible forced viscous fluid from product Einstein manifolds

We consider the fluctuation modes around a hypersurface $Σ_c$ in a $(d+2)$-dimensional product Einstein manifold, with $Σ_c$ taken either near the horizon or at some finite cutoff from the horizon. By mapping the equations that governs the lowest nontrivial order of the fluctuation modes into a system of partial differential equations on a flat Newtonian spacetime, a system of compressible, forced viscous fluid is realized. This result generalizes the non bulk/boundary holographic duality constructed by us recently to the case of a different background geometry.

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $Σ_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $Σ_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Ei…

具有Hubble半径作为红外截止的Holographic暗能量

Holographic Dark Energy with Hubble Radius as an Infrared Cutoff in Einstein-Cartan Gravity

本文研究了在爱因斯坦-卡坦引力中，以Hubble半径作为红外截止的非相互作用Holographic暗能量模型，通过推导爱因斯坦-卡坦方程并引入 torsion 标量，确定了 torsion 标量的尺度行为，并解决了之前 torsion 标量场景中的ansatz问题，从而使得宇宙加速成为可能。

Quantum corrections to finite radius holography and holographic entanglement entropy

We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two theories by mapping the flow equation of the deformed CFT to the bulk Wheeler-DeWitt equation. The latter reduces to an ordinary differential equation for the sphere partition function, which we solve to find the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere. The entanglement entropy in the inverse central charge…

全息重整化群与应力张量算符

Holographic Renormalization Group and Stress Tensor Operators

本论文围绕受$T\overline{T}$形变影响的三维反德西特引力与JT引力展开全息研究，计算相关可观测量、探索超对称扩展与一般应力张量形变，还拓展了二维外量子$T\overline{T}$算符等新方向。

On the stability of gravity with Dirichlet walls

Dirichlet walls -- timelike boundaries at finite distance from the bulk on which the induced metric is held fixed -- have been used to model AdS spacetimes with a finite cutoff. In the context of gauge/gravity duality, such models are often described as dual to some novel UV-cufoff version of a corresponding CFT that maintains local Lorentz invariance. We study linearized gravity in the presence of such a wall and find it to differ significantly from the seemingly-analogous case of Dirichlet boundary conditions for fields of spins zero and one. In particular, using the Kodama-Ishibashi formali…