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Register a new userUniversality in the stress tensor for Holographic fluids at the finite cutoff surface via fluid/gravity correspondence
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We investigate the stress tensor for holographic fluids at the finite cutoff surface through perturbing the Schwarzchild-AdS black brane background to the first order perturbations in the scenario of fluid/gravity correspondence. We investigate the most general perturbations of the metric without any gauge fixing. We consider various boundary conditions and demonstrate the properties of the corresponding holographic fluids. The critical fact is that the spatial components of the first order stress tensors of the holographic fluids can be rewritten in a concordant form, which implicates that there is an underlying universality in the first order stress tensor. We find this universality in the first order stress tensor for holographic fluids at the finite cutoff surface by an exhaustive investigation of perturbations of the full bulk metric.
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We use the subleading soft-graviton theorem to construct an operator $T_{zz}$ whose insertion in the four-dimensional tree-level quantum gravity $mathcal{S}$-matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT$_2$). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT$_2$, with the Lorentz group acting as the unbroken $SL(2,mathbb{C})$ subgroup.
We consider the tree-level scattering of massless particles in $(d+2)$-dimensional asymptotically flat spacetimes. The $mathcal{S}$-matrix elements are recast as correlation functions of local operators living on a space-like cut $mathcal{M}_d$ of the null momentum cone. The Lorentz group $SO(d+1,1)$ is nonlinearly realized as the Euclidean conformal group on $mathcal{M}_d$. Operators of non-trivial spin arise from massless particles transforming in non-trivial representations of the little group $SO(d)$, and distinguished operators arise from the soft-insertions of gauge bosons and gravitons. The leading soft-photon operator is the shadow transform of a conserved spin-one primary operator $J_a$, and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator $T_{ab}$. The universal form of the soft-limits ensures that $J_a$ and $T_{ab}$ obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFT$_d$, respectively.
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einsteins field equations, are related to the fluid dynamics, governed by the relativistic Navier-Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier-Stokes equations and soft hairy horizons.
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.
Gravity/fluid correspondence becomes an important tool to investigate the strongly correlated fluids. We carefully investigate the holographic fluids at the finite cutoff surface by considering different boundary conditions in the scenario of gravity/fluid correspondence. We find that the sonic velocity of the boundary fluids at the finite cutoff surface is critical to clarify the superficial similarity between bulk viscosity and perturbation of the pressure for the holographic fluid, where we set a special boundary condition at the finite cutoff surface to explicitly express this superficial similarity. Moreover, we further take the sonic velocity into account to investigate a case with more general boundary condition. In this more general case, two parameters in the first order stress tensor of holographic fluid cannot be fixed, one can still extract the information of transport coefficients by considering the sonic velocity seriously.
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