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Register a new userGeneralized Navier-Stokes equations and soft hairy horizons in fluid/gravity correspondence
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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.
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We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u(1) current algebras and recover the surprisingly simple entropy formula $S=2pi (J_0^+ + J_0^-)$, where $J_0^pm$ are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.
In the context of massive gravity theories, we study holographic flows driven by a relevant scalar operator and interpolating between a UV 3-dimensional CFT and an IR Kasner universe. For a large class of scalar potentials, the Cauchy horizon never forms in presence of a non-trivial scalar hair, although, in absence of it, the black hole solution has an inner horizon due to the finite graviton mass. We show that the instability of the Cauchy horizon triggered by the scalar field is associated to a rapid collapse of the Einstein-Rosen bridge. The corresponding flows run smoothly through the event horizon and at late times end in a spacelike singularity at which the asymptotic geometry takes a general Kasner form dominated by the scalar hair kinetic term. Interestingly, we discover deviations from the simple Kasner universe whenever the potential terms become larger than the kinetic one. Finally, we study the effects of the scalar deformation and the graviton mass on the Kasner singularity exponents and show the relationship between the Kasner exponents and the entanglement and butterfly velocities probing the black hole dynamics.
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.
We focus on two types of coherent states, the coherent states of multi graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find $N$-state Schrodinger cat states which approach the one-row Young tableau states, with fidelity between them asymptotically reaches 1 at large $N$. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states, and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.
Collinear and soft divergences in perturbative quantum gravity are investigated to arbitrary orders in amplitudes for wide-angle scattering, using methods developed for gauge theories. We show that collinear singularities cancel when all such divergent diagrams are summed over, by using the gravitational Ward identity that decouples the unphysical polarizations from the S-matrix. This analysis generalizes a result previously demonstrated in the eikonal approximation. We also confirm that the only virtual graviton corrections that give soft logarithmic divergences are of the ladder and crossed ladder type.
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