arXiv subjects
Publications and source records attributed to Xian-Hui Ge.
We show that field equations of some typical modified gravity theories can be recast as thermodynamic first law on dynamical holographic screens. The thermodynamic second law are also presented.
We consider the AdS$_4$ RN black hole and work out the momentum dependent hydrodynamic analysis for the vector modes. We also perform the spectral function calculation of the dual field theory. As an application, we consider the permittivity and permeability and find that for low frequency regime, the index of refraction is found to be negative, supporting the claim made in ref.\cite{amariti} for AdS$_5$. We also find that at static limit the medium has the zero permeability, a character of the superconductivity .
We investigate the holographic superconductors immersed in an external magnetic field by using the analytical approach. We obtain the spatially dependent condensate solutions in the presence of the magnetism and find analytically that the upper critical magnetic field satisfies the relation given in the Ginzburg-Landau theory. We observe analytically the reminiscent of the Meissner effect where the magnetic field expels the condensate. Extending to the D-dimensional Gauss-Bonnet AdS black holes, we examine the influence given by the Gauss-Bonnet coupling on the condensation. Different from the positive coupling, we find that the negative Gauss-Bonnet coupling enhances the condensation when the external magnetism is not strong enough.
We derive a new acoustic black hole metric from the Abelian Higgs model. In the non-relativistic limit, while the Abelian Higgs model becomes the Ginzburg-Landau model, the metric reduces to an ordinary Unruh type. We investigate the possibility of using (type I and II) superconductors as the acoustic black holes. We propose to realize experimental acoustic black holes by using spiral vortices solutions from the Navier-stokes equation in the non-relativistic classical fluids.
Motivated by the analogy between the spacetime and the solid with inhomogeneous elasticity modulus, we present an alternative method to obtain the field equation of any diffeomorphism-invariant gravity, by extremizing the constructed entropy function of the displacement vector field of spacetime solid. In general stationary spacetimes, we show that the Wald entropy of horizon arises from the on-shell entropy function of spacetime solid.
We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasi-local gravitational energy found recently for $f(R)$ gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the FRW spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for $f(R)$ gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.
We calculate the ratio of shear viscosity to entropy density for charged black branes in third order Lovelock theory. For chargeless black branes, the result turns out to be consistent with the prediction made in $\rm arXiv:0808.3498[\rm hep-th] $. We find that, the third order Lovelock gravity term does not contribute to causality violation unlike the Gauss-Bonnet term. The stability of the black brane again requires the value of the Lovelock coupling constant to be bounded by 1/4 in the infinite dimensionality limit.
We compute the dimensionality dependence of $η/s$ for charged black branes with Gauss-Bonnet correction. We find that both causality and stability constrain the value of Gauss-Bonnet coupling constant to be bounded by 1/4 in the infinite dimensionality limit. We further show that higher dimensionality stabilize the gravitational perturbation. The stabilization of the perturbation in higher dimensional space-time is a straightforward consequence of the Gauss-Bonnet coupling constant bound.
Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be $η/s=1/4π$ is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction simultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. The stability of the black brane requires the Gauss-Bonnet coupling constant $λ$($=2α'/l^2$) to be smaller than 1/24. We draw a phase diagram relevant to the instability in charge-coupling space.
We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2$ terms and $R^4$ terms are calculated as concrete examples.
We study the transport coefficients of Quark-Gluon-Plasma in finite temperature and finite baryon density. We use AdS/QCD of charged AdS black hole background with bulk-filling branes identifying the U(1) charge as the baryon number. We calculate the diffusion constant, the shear viscosity and the thermal conductivity to plot their density and temperature dependences. Hydrodynamic relations between those are shown to hold exactly. The diffusion constant and the shear viscosity are decreasing as a function of density for fixed total energy. For fixed temperature, the fluid becomes less diffusible and more viscous for larger baryon density.
From the black hole thermodynamics point of view, we show that the entropy function $\mathbf{f}$ and the free energy $F$ are related via $\mathbf{f}=e_{I}q_{I}+Ω_Hq_I{A_ϕ^I}'-\frac{\partial F}{\partial r} |_{r_{H}}$. Assuming the entropy function is known for extremal black holes, we propose an approach to calculate the entropy of non-extremal cases by slightly moving the extremal black hole geometry from extremality. The entropy of non-extremal $D1D5$- and $D1D5p$-branes in the presence of higher derivative corrections are computed as concrete examples. An attempt has also been made to explain why the entropy function method can calculate the corrected entropy without knowing the exact form of black hole solution in higher derivative gravity theories.
This paper has been withdrawn by the author due to a crucial error
We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved space-times with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking-Unruh effect. The degree of entanglement is found to be degraded with increasing the extra dimensions. For a finite black hole surface gravity, the observer may choose higher frequency mode to keep high level entanglement. The fidelity of quantum teleporation is also reduced because of the Hawking-Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.
We study a scenario of the ellipsoidal universe in the brane world cosmology with a cosmological constant in the bulk . From the five-dimensional Einstein equations we derive the evolution equations for the eccentricity and the scale factor of the universe, which are coupled to each other. It is found that if the anisotropy of our universe is originated from a uniform magnetic field inside the brane, the eccentricity decays faster in the bulk in comparison with a four-dimensional ellipsoidal universe. We also investigate the ellipsoidal universe in the brane-induced gravity and find the evolution equation for the eccentricity which has a contribution determined by the four- and five-dimensional Newton's constants. The role of the eccentricity is discussed in explaining the quadrupole problem of the cosmic microwave background.
We construct analogue black hole solutions in the braneworld scenario. The quantum fluctuations of condensate gravitons propagating around a $4+n$-dimensional gravitational potential are found yielding a metric similar to higher dimensional Schwarzschild black hole line-element. Black hole analogue solutions in Randall-Sundrum and Dvali-Gabadadze-Porrati brane world models are also constructed. The properties of such black hole analogues are discussed.
We propose that extra dimensions might be detected with higher dimensional analogues of black holes. The usual 4-dimensional acoustic(sonic)black hole metric is extended to arbitrary dimensions. The absorption cross-section of Hawking radiation on the brane and in the bulk are calculated in the semiclassical approximation.
We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Roberston-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.