Xiao-Ning Wu

Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordstrblack holes in (n + 1)-dimensional anti-de Sitter spacetime is studied in details using the thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid gas system. We first investigate critical phenomena of the RN-AdS black hole. The critical exponents of relevant thermodynamical quantities are evaluated. We find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas system. This suggests a possible universality in the phase transitions of these systems. We finally study the thermodynamic behavior using the equilibrium thermodynamic state space geometry and find that the scalar curvature diverges exactly at the van der Waals-like critical point where the heat capacity at constant charge of the black hole diverges.

Thermodynamics of Black Holes from Equipartition of Energy and Holography

A gravitational potential in the relativistic case is introduced as an alternative to Walds potential used by Verlinde, which reproduces the familiar entropy/area relation S = A/4 (in the natural units) when Verlindes idea is applied to the black hole case. Upon using the equipartition rule, the correct form of the Komar mass (energy) can also be obtained, which leads to the Einstein equations. It is explicitly shown that our entropy formula agrees with Verlindes entropy variation formula in spherical cases. The stationary space-times, especially the Kerr-Newman black hole, are then discussed, where it is shown that the equipartition rule involves the reduced mass, instead of the Amowitt-Deser-Misner mass, on the horizon of the black hole.

Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories

Abstract The dual fluid description for a general cutoff surface at radius r = r c outside the horizon in the charged AdS black brane bulk space–time is investigated, first in the Einstein–Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ϵ , the coupled Einstein–Maxwell equations are solved up to O ( ϵ 2 ) . The incompressible Navier–Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η / s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss–Bonnet–Maxwell case, where the incompressible Navier–Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η / s is independent of the cutoff r c but dependent on the charge density of the black brane.

Tunneling effect near a weakly isolated horizon

The tunneling effect near a weakly isolated horizon (WIH) has been studied. By applying the null geodesic method of Parikh and Wilczek and the Hamilton-Jacibi method of Angheben et al. to a WIH, we recover the semiclassical emission rate in the tunneling process. We show that the tunneling effect exists in a wide class of space-times admitting weakly isolated horizons. The general thermodynamic nature of WIH is then confirmed.

From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime

We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a non-vanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier–Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.

Gravitational anomaly and Hawking radiation near a weakly isolated horizon

Based on the idea of the work by Wilczek and his collaborators, we consider the gravitational anomaly near a weakly isolated horizon. We find that there exists a universal choice of tortoise coordinate for any weakly isolated horizon. Under this coordinate, the leading behavior of a quite arbitrary scalar field near a horizon is a 2-dimensional chiral scalar field. This means we can extend the idea of Wilczek and his collaborators to more general cases and show the relation between gravitational anomaly and Hawking radiation is a universal property of a black hole horizon.

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.

Fluid/gravity correspondence for general non-rotating black holes

In this paper, we investigate the fluid/gravity correspondence in spacetime with general non-rotating weakly isolated horizon. With the help of a Petrov-like boundary condition and large mean curvature limit, we show that the dual hydrodynamical system is described by a generalized forced incompressible Navier-Stokes equation. Specially, for stationary black holes or those spacetime with some asymptotically stationary conditions, such a system reduces to a standard forced Navier-Stokes system.

Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory

A bstractWe apply the membrane paradigm and the holographic Wilsonian approach to the Einstein-Gauss-Bonnet-Maxwell theory. The transport coefficients for a quark-gluon plasma living on the cutoff surface are derived in a spacetime of charged black brane. Because of the mixing of the Gauss-Bonnet coupling and the Maxwell fields, the vector modes/shear modes of the metric and Maxwell fluctuations turn out to be very difficult to decouple. We firstly evaluate the AC conductivity at a finite cutoff surface by solving the equation of motion numerically, then manage to derive the radial flow of DC conductivity with the use of the Kubo formula. It turns out that our analytical results match the numerical data in low frequency limit very well. The diffusion constant D(uc) is also derived in a long wavelength expansion limit. We find it depends on the Gauss-Bonnet coupling as well as the position of the cutoff surface.

Note on the Petrov-like boundary condition at finite cutoff surface in gravity/fluid duality

Previously it was shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near-horizon limit. In this paper, we demonstrate that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a nonrelativistic long-wavelength limit.