Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

Hawking radiation of <Emphasis Type="Italic">E</Emphasis> < <Emphasis Type="Italic">m</Emphasis> massive particles in the tunneling formalism

We use the tunneling formalism to calculate the Hawking radiation of massive particles. For E ≥ m, we recover the traditional result, identical to the massless case. But E < m particles can also tunnel across the horizon in a Hawking process. We study the probability for detecting such E < m particles as a function of the distance from the horizon and the energy of the particle in the tunneling formalism. We derive a general formula and obtain simple approximations in the near-horizon limit and in the limit of large radii.     

Vector unparticle enhanced black holes: Exact solutions and thermodynamics

Tensor and scalar unparticle couplings to matter have been shown to enhance gravitational interactions and provide corrections to the Schwarzschild metric and associated black hole structure. We derive an exact solution to the Einstein equations for vector unparticles, and conclusively demonstrate that these induce Riessner–Nordström (RN)-like solutions where the role of the “charge” is defined by a composite of unparticle phase space parameters. These black holes admit double-horizon structure, although unlike the RN metric these solutions have a minimum inner horizon value. In the extremal limit, the Hawking temperature is shown to vanish. As with the scalar/tensor case, the (outer) horizon is shown via entropy considerations to behave like a fractal surface of spectral dimension dH=2dU$d_H=2d_U$.     

An Infinite Class of Extremal Horizons in Higher Dimensions

We present a new class of near-horizon geometries which solve Einstein??s vacuum equations, including a negative cosmological constant, in all even dimensions greater than four. Spatial sections of the horizon are inhomogeneous S ²-bundles over any compact K?hler-Einstein manifold. For a given base, the solutions are parameterised by one continuous parameter (the angular momentum) and an integer which determines the topology of the horizon. In six dimensions the horizon topology is either S ²?× S ² or ${\mathbb{CP}^2\# \overline{\mathbb{CP}^2}}$ . In higher dimensions the S ²-bundles are always non-trivial, and for a fixed base, give an infinite number of distinct horizon topologies. Furthermore, depending on the choice of base we can get examples of near-horizon geometries with a single rotational symmetry (the minimal dimension for this is eight). All of our horizon geometries are consistent with all known topology and symmetry constraints for the horizons of asymptotically flat or globally Anti de Sitter extremal black holes.     

The incompressible Navier–Stokes equations from black hole membrane dynamics

We consider the dynamics of a d+1 space–time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de Sitter space–time and show that it is described by the d-dimensional incompressible Navier–Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier–Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.     

On EVH black hole solution in heterotic string theory

We study the near horizon geometry of charged rotating black holes in toroidal compactifications of heterotic string theory. We analyze the extremal vanishing horizon (EVH) limit for these black hole solutions and we will show that the near horizon geometry develops an AdS₃ throat. Furthermore, we will show that the near horizon limit of near EVH black holes has a BTZ factor. We also comment on the CFT dual to this near horizon geometry.     

Solution and ellipticity properties of the self-duality equations of Corriganet al. in eight dimensions

We study the two sets of self-dual Yang-Mills equations in eight dimensions proposed in 1983 by E. Corriganet at. and show that one of these sets forms an elliptic system under the Coulomb gauge condition, and the other (overdetermined) set can have solutions that depend at most onN arbitrary constants, whereN is the dimension of the gauge group, hence the global solutions of both systems are finite dimensional. We describe a subvarietyP ₈ of the skew-symmetric 8 x 8 matrices by an eigenvalue criterion and we show that the solutions of the elliptic equations of Corriganet al. are among the maximal linear submanifolds ofP ₈. We propose an eighth-order action for which the elliptic set is a maximum.     

Bethe-ansatz solution of a model for a mixed valent impurity with two magnetic configurations: II. Numerical solution of the thermodynamic equations

A mixed valence impurity with two magnetic configurations of total angular momentumJ ₂ andJ ₁=J ₂+1/2, respectively, coupled by conduction electrons with total angular momentum 1/2 via a hybridization matrix element is considered. The thermodynamic Bethe-ansatz equations derived previously are solved numerically for various values ofJ ₂. Thef-level occupation, the entropy, the magnetic susceptibility and the specific heat are obtained as a function of temperature for variousf-level positions. The magnetic field dependence is also discussed in the limit of integer valence (exchange model).Supported by the CONICET, Argentina     

Thermodynamics of regular black hole

We investigate thermodynamics for a magnetically charged regular black hole (MCRBH), which comes from the action of general relativity and nonlinear electromagnetics, comparing with the Reissner–Norström (RN) black hole in both four and two dimensions after dimensional reduction. We find that there is no thermodynamic difference between the regular and RN black holes for a fixed charge Q in both dimensions. This means that the condition for either singularity or regularity at the origin of coordinate does not affect the thermodynamics of black hole. Furthermore, we describe the near-horizon AdS₂ thermodynamics of the MCRBH with the connection of the Jackiw–Teitelboim theory. We also identify the near-horizon entropy as the statistical entropy by using the AdS₂/CFT₁ correspondence.     

Effective Lagrangian for quantum black holes

We discuss the most general effective Lagrangian obtained from the assumption that the degrees of freedom to be quantized, in a black hole, are on the horizon. The effective Lagrangian depends only on the induced metric and the extrinsic curvature of the (fluctuating) horizon, and the possible operators can be arranged in an expansion in powers of M_P1/M, where M_P1 is the Planck mass and M the black hole mass. We perform a semiclassical expansion of the action with a formalism which preserves general covariance explicitly. Quantum fluctuations over the classical solutions are described by a single scalar field living in the (2 + 1)-dimensional world-volume swept by the horizon, with a given coupling to the background geometry. We discuss the resulting field theory and we compute the black hole entropy with our formalism.     

On homogenization and scaling limit of some gradient perturbations of a massless free field

We study the continuum scaling limit of some statistical mechanical models defined by convex Hamiltonians which are gradient perturbations of a massless free field. By proving a central limit theorem for these models, we show that their long distance behavior is identical to a new (homogenized) continuum massless free field. We shall also obtain some new bounds on the 2-point correlation functions of these models. This article was processed by the author using the LAT_EX style filepljour1 from Springer-Verlag.     

Relationship between the parting limit for de-alloying and a particular geometric high-density site percolation threshold

The parting limit or de-alloying threshold for electrolytic dissolution of the more reactive component from a homogeneous fcc binary alloy is usually between 50 and 60 at%. The system that has been most studied, dissolution of Ag from Ag–Au, shows a parting limit close to 55 at% Ag. Here, Kinetic Monte Carlo (KMC) simulations of ‘Ag–Au’ alloys and geometric percolation modeling are used to study the relationship between this parting limit and the high-density site percolation thresholds p _c(m) for an fcc lattice, subject to the rule that atoms with coordination greater than nine are prevented from dissolution. The value of p _c(9) is calculated from geometric considerations to be 59.97 ± 0.03%. In comparison, using KMC simulations with no surface diffusion and no dissolution allowed for ‘Ag’ atoms with more than nine total neighbors, the parting limit is found to be slightly lower (58.4 ± 0.1%). This slight discrepancy is explained by consideration of the local atomic configurations of ‘Ag’ atoms – a few of these configurations satisfy the percolation requirement but do not sustain de-alloying, while a larger number show the converse behavior. There is still, however, an underlying relationship between the parting limit and the percolation threshold, because being at p _c(9) guarantees a percolation path in which successive ‘Ag’ atoms share at least one other ‘Ag’ neighbor. With realistic kinetics of surface diffusion for ‘Au’, the parting limit drops to 54.7 ± 0.3% because a few otherwise inaccessible dissolution paths are opened up by surface diffusion of ‘Au’.     

Gravitational geons on the brane

In this paper, we examine the possibility of static, spherically symmetric gravitational geons on a 3 dimensional brane embedded in a 4+1 dimensional space-time. We choose a specific g _tt for the brane-world space-time metric. We then calculate g _rr analytically in the weak field limit and numerically for stronger fields. We show that the induced field equations on the brane do admit gravitational geon solutions.     

U(1)×SU(2)-gauge invariance of non-relativistic quantum mechanics,and generalized Hall effects

We show that the non-relativistic quantum mechanics of particles with spin coupled to an electromagnetic field has a naturalU(1)×SU(2) gauge invariance. Ward identities reflecting this gauge invariance combined with an assumption of incompressibility of a system of such particles in an appropriate external field and for suitable values of the particle density permit us to determine the form of the effective action of the system as a functional of small fluctuations in the electromagnetic field, in the large-distance-, adiabatic limit. In this limit, the action is found to have a universal form. We present explicit results for two-dimensional, incompressible electron fluids and apply them to derive the equations of linear response theory, describing a variety of generalized Hall effects. Sum rules for the Hall conductivities, magnetic susceptibilities and other quantities of physical interest are found.     

Theory of Gravitational-Inertial Field of Universe

In this paper the basic proposition is a generalization of the metric tensor by introduction of an inertial field tensor satisfying ?_ig_lm ? g_lm;i ≠ 0. On the basis of variational equations a system of more general covariant equations of gravitational-inertial field is obtained. In Einstein's approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems of generl taheory of relativity by means of the new equations give the same results as Einstein's equations. However application of these equations to the cosmologic problem leads to following results: 1. All Galaxies in the Universe (actually all bodies if gravitational attraction is not considered) “disperse” from each other according to Hubble's law. Thus contrary to Friedmann's theory (according to which the “expansion of Universe” began from the singular state with an infinite velocity) the velocity of “dispersion” of bodies begins from the zero value and in the limit tends to the velocity of light. 2. The “dispertion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free bodies in the inertial field - the law of inertia. All critical systems (with Schwarzschild radius) are specific because they exist in maximal inertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In the high-potential inertial and gravitational fields the material mass in a static state or in the process of motion with decelleration is subject to an inertial and gravitational “annihilation”. Under the maximal value of inertial and gravitational potentials (= c²) the material mass is completely “evaporated” transforming into a radiation mass. The latter is concentrated in the “horizon” of the critical system. All critical systems –“black holes”- represent geon systems, i.e., the local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown. The Universe is in a state of dynamical equilibrium. Near the external part of its boundary surface a transformation of matter into electromagnetic-gravitational-neutrineal energy (geon mass) takes place. Inside the Universe, in the galaxies takes place the synthesis of matter from geon mass, penetrating from the external part of the world (from geon crown) by means of a tunneling mechanism. The geon system may be considered as a natural entire cybernetic system.     

f(R,L m ) gravity

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L _m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.     

From massive gravity to modified general relativity

Massive gravity which has been constructed from a cohomological formulation of gauge invariance by means of the descent equations is here investigated in the classical limit. Gauge invariance requires a vector-graviton field v coupled to the massive tensor field h _μν . In the limit of vanishing graviton mass the v-field does not decouple. On the classical level this leads to a modification of general relativity. The contribution of the v-field to the energy-momentum tensor can be interpreted as dark matter density and pressure. We solve the modified field equations in the simplest spherically symmetric geometry.     

Effective action for the Yukawa2 quantum field theory

Using a rigorous version of the renormalization group we construct the effective action for theY ₂ model. The construction starts with integrating out the bosonic field which eliminates the large fields problem. Studying the soobtained purely fermionic theory proceeds by a series of convergent perturbation expansions. We show that the continuum limit of the effective action exists and its perturbation expansion is Borel summable.