arXiv subjects

Yu Tian

Publications and source records attributed to Yu Tian.

At least 379 records · Page 21Linked to original sources

arXiv2012

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.

hep-th↗

arXiv2012

Fluid/gravity duality with Petrov-like boundary condition in a spacetime with a cosmological constant

Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov type I condition on the boundary should be equivalent to the conventional method using the hydrodynamical expansion of the metric in the near horizon limit.

hep-th↗

arXiv2012

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

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.

hep-th↗

arXiv2012

Geometries with the second Poincaré symmetry

The second Poincaré kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincaré symmetry is presented and their properties are analyzed. On the geometries, the new mechanics based on the principle of relativity with two universal constants $(c,l)$ can be established.

gr-qc↗

arXiv2012

New Geometry with All Killing Vectors Spanning the Poincaré Algebra

The new 4D geometry whose Killing vectors span the Poincaré algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincaré-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological space-time with a Lobachevsky space. The motion of free particles in the space-time is discussed.

gr-qc↗

arXiv2012

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

We 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 $D(u_c)$ 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.

hep-th↗

arXiv2012

A discussion on "generality of shear thickening in dense suspensions"

In a recent Nature Materials article, Brown et al. reported a generality of shear thickening in dense suspensions and demonstrated that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased to below a threshold. However, the generality of the shear thickening reported in the article may not be necessary true when a high electric/magnetic field is applied on an ER/MR fluid. Shear thickening of ER fluid and MR fluid under high electric/magnetic fields at low shear rates, indicating an obvious phase change inside the dense suspensions has been observed.

cond-mat.soft↗

arXiv2011

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 nonvanishing 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.

gr-qc↗

arXiv2011

Some Peculiarities of Newton-Hooke Space-Times

Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on the Lagrangian/action formalism is performed in the discussion of the Newton-Hooke quantum mechanics, where the path integral point of view plays an important role, and the physically measurable density of probability is clarified.

math-ph↗

arXiv2011

Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

The phase transition of Reissner-Nordström black 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.

hep-th↗

arXiv2011

Thermodynamics on the Maximally Symmetric Holographic Screen and Entropy from Conical Singularities

For a general maximally symmetric (spherically, plane or hyperbola symmetric) holographic screen, we rewrite the equations of motion of general Lovelock gravity into the form of some generalized first law of thermodynamics, under certain ansatz. With this observation together with other two independent ways, exactly the same temperature and entropy on the screen are obtained. So it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general maximally symmetric screen. Moreover, the formula of entropy is further checked in the (maximally symmetric) general static case and dynamical case. The entropy formula also holds for those cases. Finally, the method of conical singularity is used to calculate the entropy on such screen, and the result again confirms the entropy formula.

hep-th↗

arXiv2011

Dynamics of Gravity as Thermodynamics on the Spherical Holographic Screen

The dynamics of general Lovelock gravity, viewed on an arbitrary spherically symmetric surface as a holographic screen, is recast as the form of some generalized first law of thermodynamics on the screen. From this observation together with other two distinct aspects, where exactly the same temperature and entropy on the screen arise, it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general spherically symmetric screen.

hep-th↗

arXiv2010

Reversible shear thickening at low shear rates of electrorheological fluids under electric fields

Shear thickening is a phenomenon of significant viscosity increase of colloidal suspensions. While electrorheological (ER) fluids can be turned into a solid-like material by applying an electric field, their shear strength is widely represented by the attractive electrostatic interaction between ER particles. By shearing ER fluids between two concentric cylinders, we show a reversible shear thickening of ER fluids above a low critical shear rate (<1 s-1) and a high critical electric field strength (>100 V/mm), which could be characterized by a modified Mason number. Shear thickening and electrostatic particle interaction-induced inter-particle friction forces is considered to be the real origin of the high shear strength of ER fluids, while the applied electric field controls the extent of shear thickening. The electric field-controlled reversible shear thickening has implications for high-performance ER/magnetorheological (MR) fluid design, clutch fluids with high friction forces triggered by applying local electric field, other field-responsive materials and intelligent systems.

cond-mat.soft↗

arXiv2010

Geometries for Possible Kinematics

The algebras for all possible Lorentzian and Euclidean kinematics with $\frak{so}(3)$ isotropy except static ones are re-classified. The geometries for algebras are presented by contraction approach. The relations among the geometries are revealed. Almost all geometries fall into pairs. There exists $t \leftrightarrow 1/(ν^2t)$ correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.

math-ph↗

arXiv2010

Thermodynamics of Black Holes from Equipartition of Energy and Holography

A gravitational potential in the relativistic case is introduced as an alternative to Wald's potential used by Verlinde, which reproduces the familiar entropy/area relation S=A/4 (in the natural units) when Verlinde's 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 Verlinde's 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 ADM mass, on the horizon of the black hole.

hep-th↗

arXiv2009

Extremal Isolated Horizon/CFT Correspondence

The near-horizon limit of the extremal (weakly) isolated horizon is obtained under the Bondi-like coordinates. For the vacuum case, explicit coordinate transformation relating the near-horizon metric under the Bondi-like coordinates and the standard Poincaré-type or global near-horizon metric of the extremal Kerr black hole is found, which shows that the two geometries are the same. Combined with the known thermodynamics of the (weakly) isolated horizon, it is argued that the Kerr/CFT correspondence can be generalized to the case of a large class of non-stationary extremal black holes.

hep-th↗

arXiv2008

Acceleration-extended Newton-Hooke symmetry and its dynamical realization

Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration, as well as central charges. We consider a higher order Lagrangian that is quasi-invariant under the acceleration-extended Newton-Hooke symmetry, and obtain the Schrödinger equation quantizing the Hamiltonian corresponding to its first order form. We show that the Schrödinger equation is invariant under the acceleration-extended Newton-Hooke transformations. We also discuss briefly the exotic conformal Newton-Hooke symmetry in 2+1 dimension.

hep-th↗

arXiv2008

On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity

It is shown that all vacuum solutions of Einstein field equation with a positive cosmological constant are the solutions of a model of dS gauge theory of gravity. Therefore, the model is expected to pass the observational tests on the scale of solar system and explain the indirect evidence of gravitational wave from the binary pulsars PSR1913+16.

gr-qc↗