Which coordinate representations can give correct Hawking temperature of Kerr black hole by tunneling approach

Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x_(t)^m{{\xi_{(t)}^\mu}} and x_(j)^m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function.     

Thermal States in Conformal QFT. I

We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A{{\mathcal A}} of von Neumann algebras on \mathbb R{\mathbb R} . In this first part, we focus on the completely rational net A{{\mathcal A}} . Our main result here states that, if A{{\mathcal{A}}} is completely rational, there exists exactly one locally normal KMS state j{\varphi} . Moreover, j{\varphi} is canonically constructed by a geometric procedure. A crucial r?le is played by the analysis of the “thermal completion net” associated with a locally normal KMS state. A similar uniqueness result holds for KMS states of two-dimensional local conformal nets w.r.t. the time-translation one-parameter group.     

Letter: An Einstein-Like Theory of Gravity with a Non-Newtonian Weak-Field Limit

We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as ln & ThinSpace;r. The Newtonian term GM/r appears only as subleading. Our model can be used to give a phenomenological explanation of the rotation curves of the galaxies without postulating the presence of dark matter. This can be achieved only by giving up the Einstein equivalence principle at galactic scales.     

Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity models with curvature–matter coupling

A modified f(G) gravity model with coupling between matter and geometry is proposed, which is described by the product of the Lagrange density of the matter and an arbitrary function of the Gauss–Bonnet term. The field equations and the equations of motion corresponding to this model show the non-conservation of the energy-momentum tensor, the presence of an extra force acting on test particles and non-geodesic motion. Moreover, the energy conditions and the stability criterion at the de Sitter point in modified f(G) gravity models with curvature–matter coupling are derived, which can degenerate to the well-known energy conditions in general relativity. Furthermore, in order to get some insight in the meaning of these energy conditions, we apply them to the specific models of f(G) gravity and the corresponding constraints on the models are given. In addition, the conditions and the candidate for late-time cosmic accelerated expansion in modified f(G) gravity are studied by means of conditions of power-law expansion and the equation of state of matter ω smaller than -\frac13-\frac{1}{3}.     

Protecting the Conformal Symmetry via Bulk Renormalization on Anti deSitter Space

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field j{\varphi} on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field f{\phi} on d + 1-dimensional Anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the one-loop “fish diagram” on AdS₄ by differential renormalization, and calculate the anomalous dimension of the composite boundary field j²{\varphi^2} with bulk interaction kf⁴{\kappa \phi^4}.     

Unifying dark energy and dark matter with the modified Ricci model

In this paper, two modified Ricci models are considered as the candidates of unified dark matter–dark energy. In model one, the energy density is given by r_MR=3M_pl(aH²+b[(H)\dot])\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\alpha H^{2}+\beta\dot{H}), whereas, in model two, by r_MR=3M_pl(\fraca6 R+g[(H)\ddot]H^-1)\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\frac{\alpha}{6} R+\gamma\ddot{H}H^{-1}). We find that they can explain both dark matter and dark energy successfully. A constant equation of state of dark energy is obtained in model one, which means that it gives the same background evolution as the wCDM model, while model two can give an evolutionary equation of state of dark energy with the phantom divide line crossing in the near past.     

Extended Birkhoff’s theorem in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, Eur. Phys. J. (2011), ], we prove that Birkhoff’s theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss, respectively, the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of Birkhoff’s theorem in the frame of f(T) gravity via a conformal transformation by regarding the Brans–Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.     

Dielectric spectroscopy study of the new compound [C<Subscript>12</Subscript>H<Subscript>17</Subscript>N<Subscript>2</Subscript>]<Subscript>2</Subscript>CdCl<Subscript>4</Subscript>

The temperature dependence of the electrical conductivity of the compound 2,4,4-trimethyl-4,5-dihydro-3H-benzo[b] [1,4] diazepin-1-ium tetrachlorocadmiate in the different phases follows the Arrhenius law. The imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism. In the temperature range 348–394 K, the activation energy of conductivity obtained from complex permittivity in regions I and II are, respectively, 1.03 and 0.33 eV, and E _m (in regions I and II are, respectively, 0.97 and 0.36 eV) obtained from the modulus spectra is close, suggesting that the ion transport is probably due to a hopping mechanism. The Kohlrausch–Williams–Watts function, j(t) = exp( - ( \fractt_\textKWW )^b ) \varphi (t) = \exp \left( { - {{\left( {\frac{t}{{{\tau_{\text{KWW}}}}}} \right)}^\beta }} \right) , and the coupling model are utilized for analyzing electric modulus at various temperatures. The decreasing of β at 373 K is due to approaching the temperatures of change in the conduction mechanism of the sample.     

The Interaction of a Gap with a Free Boundary in a Two Dimensional Dimer System

Let ℓ be a fixed vertical lattice line of the unit triangular lattice in the plane, and let H{\mathcal{H}} be the half plane to the left of ℓ. We consider lozenge tilings of H{\mathcal{H}} that have a triangular gap of side-length two and in which ℓ is a free boundary — i.e., tiles are allowed to protrude out half-way across ℓ. We prove that the correlation function of this gap near the free boundary has asymptotics \frac14pr{\frac{1}{4\pi r}}, r → ∞, where r is the distance from the gap to the free boundary. This parallels the electrostatic phenomenon by which the field of an electric charge near a conductor can be obtained by the method of images.     

Can Inflation, Dark Matter and Dark Energy Be Described in Terms of a Single, Real Scalar Field?

In this article, our aim is to consider inflation, dark energy and dark matter in the framework of a real scalar field. To this end, we use the quintessence approach. We have tried a real scalar field with a specific self-interaction potential in a spacially flat universe. Numerical results indicate that this potential can drive the expansion of the universe in three distinct phases. The first phase behaves as an inflationary expansion. For this stage, setting the scalar field’s initial value to ϕ ₀≥1.94 leads to N 3 68\mathcal{N}\geq 68 favored by observation. After the inflationary phase, the scalar field starts an oscillatory behavior which averages to a =0\bar{w}=0 fluid. This stage can be taken as a cold dark matter (p≈0) epoch expected from works on the structure formation issue. Observations and cosmological models indicate that t _inf ≈10⁻³⁵ s and the matter dominated lasts for t _m ≈10¹⁷ s, hence (\fract_mt_inf)_obs ? 10⁵²(\frac{t_{m}}{t_{inf}})_{obs}\approx10^{52}. We have shown that the present model can satisfy such a constraint. Finally, the scalar field leaves the oscillatory behavior and once again enters a second inflationary stage which can be identified with the recent accelerated expansion of the universe. We have also compared our model with the ΛCDM model and have found a very good agreement between the equation of state parameter of both of models during the DM and DE era.     

Inertial-Range Behavior of a Passive Scalar Field in a Random Shear Flow: Renormalization Group Analysis of a Simple Model

Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form μ d(t-t￠) / k_^^d-1+x\propto\delta(t-t') / k_{\bot}^{d-1+\xi}, where k _⊥=|k _⊥| and k _⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum E μ k_^^1-e\mathcal{E} \propto k_{\bot}^{1-\varepsilon} and in the dispersion law w μ k_^^2-h\omega\propto k_{\bot}^{2-\eta}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray η=0, ε>0 in the ε–η plane. The physical (Kolmogorov) point ε=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.     

Influence of Gauss-Bonnet Coupling Parameter on?the?Thermodynamic Properties of?Einstein-Gauss-Bonnet and?Einstein-Yang-Mills-Gauss-Bonnet Black Holes

This paper deals in the thermodynamic properties of Einstein-Gauss-Bonnet and Einstein-Yang-Mills-Gauss-Bonnet black holes. It exhibits the various stable and unstable phases of the black holes in these two modified gravity theories. In the first section, that reveals the various aspects of Einstein-Gauss-Bonnet black holes, we chose to study the changes in the Hawking Temperature with variations in the radius of event horizon (r) and charge (Q); and tried to justify them physically. Secondly in case of Einstein-Yang-Mills-Gauss-Bonnet black holes, we have attempted to compare the changes in the various thermodynamic parameters with varying r and Q; with the Einstein-Gauss-Bonnet black holes at a macroscopic level. Here we have considered the Yang Mills tensor, electromagnetic Lagrangian added to the action integrand. Again this very work deals in drawing out the similarities between these two types of black holes, thereby throwing some light on the aspect of black hole stability. Later we have also introspected the effects of the Gauss-Bonnet coupling parameter α, whose function (6αr), is added as a correction term to the black hole entropy. We have especially focused on what changes does it have upon the nature of the plots as to whether it enhances or reduces the effect of Q on the behavior of the curves. Finally this paper has also kept an eye at estimating the stability domains of the black holes described in these two gravity theories.     

Thermodynamic Formalism for Contracting Lorenz Flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential [^( j)]_t(x,y,z):=-tlogJ_(x,y,z)^cu\hat{ \varphi }_{t}(x,y,z):=-t\log J_{(x,y,z)}^{cu} for the contracting Lorenz flow and for t in an interval containing [0,1]. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.     

Dilaton Dark Energy Model in f(R), f(T) and Ho?ava-Lifshitz Gravities

In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories, namely f(R),f(T) and Hořava-Lifshitz gravities and analyzed the behavior of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein’s gravity. In f(R) and f(T) gravities, we have considered some particular forms of f(R) and f(T) and we have shown that the potentials always increase with the dilaton fields. But in Hořava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.     

Static spherically symmetric solution of (<Emphasis Type="Italic">R</Emphasis> ± <Emphasis Type="Italic">μ</Emphasis><Superscript>4</Superscript>/<Emphasis Type="Italic">R</Emphasis>) gravity

The static spherically symmetric solution for R ± μ ⁴/R model of f(R) gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when μ tends to zero. For the obtained metric, the deviation from Einstein gravity is very small. This result is different from the other results have been obtained by equivalence between f(R) gravity and scalar tensor theory. Also it is shown that the vacuum solution in the solar system depends on the shape of matter distribution which differ from the Einstein’s gravity.     

Potential–density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential–density pairs to describe axi-symmetric galaxies in the Newtonian limit of scalar–tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential–density pairs of galactic disks for an exponential profile and their rotation curves.     

Theoretical study of the dynamics for the H + Li H ( v = 0, j = 0) $\to$ H2 + Li reaction and its isotopic variants

Quasi-classical trajectory (QCT) method is carried out to calculate the dynamics of the H + LiH (v = 0, j = 0) ?\to H₂ + Li reaction and its isotopic variants based on the potential energy surface of the lowest ²A￠^2A' electronic state reported by Prudente et al. [Chem. Phys. Lett. 474, 18 (2009)]. The reaction cross-section, product rotational alignment parameter áP₂\langle P_2 ([(j￠)\vec]\vec{j'} ·\cdot [(k)\vec])?\vec{k})\rangle and one generalized polarization-dependent differential cross-section (2π/σ)(ds₀₀d\sigma_{00}/d w_t\omega_t) are calculated. We found that different collision energies and mass factors show driving influence on the process of the reactions and product molecules H₂ (HD, D₂) polarization distribution, and the trend of the isotopic effects in the high collision energy range is different to that in the low collision energy range. The calculations are also interpreted in relation to the features of the underlying potential energy surface. A comparison between the title reactions and a barrier-less reaction F + HBr ?\to FH + Br has been discussed in detail.     

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure F(R) gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-Λ-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-Λ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure F(R) gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at r = 0. We should note that the Kreschmann scalar of charged solutions goes to infinity as r → 0, but with a rate slower than that of uncharged solutions.