Charged rotating dilaton black branes in AdS universe

We present the metric for the (n + 1)-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.     

Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

In the “braneworld scenario” ordinary standard model matter and non-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the ‘bulk’ (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Assuming that the lapse function may either be a constant or a function of both time and of the extra coordinates, we have studied the nature of the geodesics of test particles and photons and have analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

Generalised splitting of spacetime

Normally, when a spacetime splitting is considered the ADM 3+1 split is brought to mind. In this paper, the idea of spacetime splitting is extended to include anm + n splitting of spacetime. The global spacetime has dimension (m + n) and the foliating spaces have dimensionm. There aren independent normals to each of these foliating spaces, thus givingn different extrinsic curvatures. The generalised Gauss-Weingarten and the generalised Gauss-Codazzi equations associated with this splitting are derived. These generalised equations reduce to the familar ADM equations when a 3+1 split is considered. The generalised equations are found to have a particularly elegant form when an orthogonal splitting of spacetime is examined.     

Influence of a brane tension on phantom and massive scalar field emission

We elaborate the signature of the extra dimensions and brane tension in the process of phantom and massive scalar emission in the spacetime of (4 + n)-dimensional tense brane black hole. Absorption cross section, luminosity of Hawking radiation and cross section in the low-energy approximation were found. We envisage that parameter connected with the existence of a brane imprints its role in the Hawking radiation of the considered fields.     

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus, one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena that can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.     

Living with phantoms fields in a sheet spacetime

We consider the flat anisotropic Bianchi I braneworld model of the universe within the framework of low energy effective string action in four-dimensions including the leading order α′ terms, two-scalar fields, their interaction, non-minimal coupling of the dark-energy scalar field to the scalar curvature and effective cosmological constant. Backward (high energy limit) and forward (low energy limit) in time analytic solutions are derived and late-time accelerated expansion was found. It is shown that during the transition from high energy limit to the low energy limit, the topology of the universe is changing in time: we have a transition from a (1 + 3) FRW homogenous and isotropic spacetime dominated by radiation to a (1 + 2) spacetime sheet dominated by phantom energy while the third spatial dimension is contracted in time. We have also found that dark matter and dark energy may be unified at early epoch in the form of radiation fluids while the late-time dynamics is governed by phantom energy and dark energy. Many interesting features are revealed.     

Existence and Modulation of Uniform Sliding States in Driven and Overdamped Particle Chains

In this paper we are mainly concerned with existence and modulation of uniform sliding states for particle chains with damping γ and external driving force F. If the on-site potential vanishes, then for each F > 0 there exist trivial uniform sliding states x _n (t) = n ω + ν t + α for which the particles are uniformly spaced with spacing ω > 0, the sliding velocity of each particle is ν = F/γ, and the phase α is arbitrary. If the particle chain with convex interaction potential is placed in a periodic on-site potential, we show under some conditions the existence of modulated uniform sliding states of the form

Moment Matrices and Multi-Component KP,with Applications to Random Matrix Theory

Questions on random matrices and non-intersecting Brownian motions have led to the study of moment matrices with regard to several weights. The main result of this paper is to show that the determinants of such moment matrices satisfy, upon adding one set of “time” deformations for each weight, the multi-component KP-hierarchy: these determinants are thus “tau-functions” for these integrable hierarchies. The tau-functions, so obtained, with appropriate shifts of the time-parameters (forward and backwards) will be expressed in terms of multiple orthogonal polynomials for these weights and their Cauchy transforms. The main result is a vast generalization of a known fact about infinitesimal deformations of orthogonal polynomials: it concerns an identity between the orthogonality of polynomials on the real line, the bilinear identity in KP theory and a generating functional for the full KP theory. An additional fact not discussed in this paper is that these τ-functions satisfy Virasoro constraints with respect to these time parameters. As one of the many examples worked out in this paper, we consider N non-intersecting Brownian motions in leaving from the origin, with n _i particles forced to reach p distinct target points b _i at time t  =  1; of course, . We give a PDE, in terms of the boundary points of the interval E, for the probability that the Brownian particles all pass through an interval E at time 0  <  t  <  1. It is given by the determinant of a (p + 1)  ×  (p + 1) matrix, which is nearly a wronskian. This theory is also applied to biorthogonal polynomials and orthogonal polynomials on the circle. The support of a National Science Foundation grant # DMS-07-04271 is gratefully acknowledged. The support of a National Science Foundation grant # DMS-07-04271, a European Science Foundation grant (MISGAM), a Marie Curie Grant (ENIGMA), a FNRS grant and a “Interuniversity Attraction Pole” grant is gratefully acknowledged. The support of a European Science Foundation grant (MISGAM), a Marie Curie Grant (ENIGMA) and a ANR grant (GIMP) is gratefully acknowledged.     

Effects of the quantization ambiguities on the Big Bounce dynamics

In this paper, we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator F̂ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantization. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a two-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parameterized by the canonical variable p (or by the scale factor a). We demonstrate that the evolutional scenario depends on the geometrical constant parameter Λ as well as the model parameter n. We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. The values of the parameter n and the cosmological constant differentiate asymptotic states of the evolution. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the de Sitter contracting (deS₋) spacetime or the static Einstein universe H = 0 or H =  − ∞ state and reaches the de Sitter expanding state (deS₊), the state H = 0 or H =  + ∞ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.     

CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds

In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h ? [-1,-\frac2?{n-1}n)h\in[-1,-\frac{2\sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of S₁^n-1×\mathbbRS_1^{n-1}\times \mathbb{R} in the (n + 1)-dimensional de Sitter space S₁ⁿ⁺¹\hbox{\bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.     

Microhydration of the methylene blue cation in an electrospray ion source

Microhydrated methylene blue cations, MB⁺(H₂O) _n , are produced in an electrospray ion source and their size-distributions are measured as a function of the source temperature. A series of MB⁺(H₂O) _n ions is observed up to n ≃ 60. A striking feature observed in the mass spectra is that the series of hydrated ions starts at n = 4; intensities of n = 1–3 are extremely suppressed. The absence of n = 1–3 ions is well explained by the energetics concerning evaporation processes of water molecules, based on stable structures and the binding energies of MB⁺(H₂O) _n ions calculated by DFT calculations up to n = 5. MB⁺(H₂O) _n ions for n > 4 evaporate a single water molecule sequentially, while MB⁺(H₂O)₄ tends to fragment into MB⁺ and (H₂O)₄ rather than MB⁺(H₂O)₃ and an H₂O molecule. We have observed a clear magic peak at n = 24, which strongly suggests that the MB⁺(H₂O)₂₄ ion is formed by attaching a neutral (H₂O)₂₀ cage onto an MB⁺(H₂O)₄ ion.     

Fluctuations of the Nodal Length of Random Spherical Harmonics

Using the multiplicities of the Laplace eigenspace on the sphere (the space of spherical harmonics) we endow the space with Gaussian probability measure. This induces a notion of random Gaussian spherical harmonics of degree n having Laplace eigenvalue E = n(n + 1). We study the length distribution of the nodal lines of random spherical harmonics.     

Higher-dimensional perfect fluids and empty singular boundaries

In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein’s equations consisting in a (N + 2)-dimensional static and hyperplane symmetric perfect fluid satisfying the equation of state ρ = ηp, being η an arbitrary constant and N ≥ 2. We show that this spacetime has some weird properties. In particular, in the case η > −1, it has an empty (without matter) repulsive singular boundary. We also study the behavior of geodesics and the Cauchy problem for the propagation of massless scalar field in this spacetime. For η > 1, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at z = ∞; whereas non-vertical null as well as all time-like ones are bounded between two planes determined by initial conditions. We obtain that the Cauchy problem for the propagation of a massless scalar field is well-posed and waves are completely reflected at the singularity, if we only demand the waves to have finite energy, although no boundary condition is required.     

<Emphasis Type="Italic">L</Emphasis><Subscript>∞</Subscript>-Algebras from Multisymplectic Geometry

A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n + 1. In previous work with Baez and Hoffnung, we described how the ‘higher analogs’ of the algebraic and geometric structures found in symplectic geometry should naturally arise in 2-plectic geometry. In particular, just as a symplectic manifold gives a Poisson algebra of functions, any 2-plectic manifold gives a Lie 2-algebra of 1-forms and functions. Lie n-algebras are examples of L _∞-algebras: graded vector spaces equipped with a collection of skew-symmetric multi-brackets that satisfy a generalized Jacobi identity. Here, we generalize our previous result. Given an n-plectic manifold, we explicitly construct a corresponding Lie n-algebra on a complex consisting of differential forms whose multi-brackets are specified by the n-plectic structure. We also show that any n-plectic manifold gives rise to another kind of algebraic structure known as a differential graded Leibniz algebra. We conclude by describing the similarities between these two structures within the context of an open problem in the theory of strongly homotopy algebras. We also mention a possible connection with the work of Barnich, Fulp, Lada, and Stasheff on the Gelfand–Dickey–Dorfman formalism.     

Photon emission from clean and oxygenated Si and SiO2 surfaces bombarded by 5 keV krypton ions

The effect of oxygen on the light emission from a Si (1 0 0) semiconductor bombarded by energetic Kr⁺ ions has been studied in the 200–300 nm wavelength range. The influence of oxygen was verified by studying the optical spectra of SiO₂ bombarded under similar experimental conditions. It has been found that the measured intensities of the emitted photons are always higher in the presence of oxygen, even higher than those obtained for SiO₂. The electron-transfer model can explain our experimental observations. We do believe that in the presence of oxygen, an intermediate structure of silicon sub-oxide SiO_X<2 is formed on silicon surface, which is responsible for the increase of photon emission. In addition, the radiative dissociation process and breaking of chemical bond seems contribute to the enhancement of emitted photons intensity.     

Proof of the Julia–Zee Theorem

It is a well accepted principle that finite-energy static solutions in the classical relativistic gauge field theory over the (2 + 1)-dimensional Minkowski spacetime must be electrically neutral. We call such a statement the Julia–Zee theorem. In this paper, we present a mathematical proof of this fundamental structural property.     

D-branes from classical macroscopic strings

This paper is a sequel to the series of papers dedicated to model independent analysis of brane-like extended objects in curved backgrounds. In particular, we study cylindrical membranes wrapped around the extra compact dimension of a (D + 1)-dimensional Riemann–Cartan spacetime. The world-sheet equations are obtained from the universally valid conservation equations of the membrane stress–energy and spin tensors. In the limit of small extra dimension, the dimensionally reduced theory is obtained. The narrow membrane becomes an effective string characterized not only by tension and spin, but also by electric and dilaton charges. The boundary of such an effective string has been shown to live in less spacetime dimensions than its interior. Precisely, the string endpoints are trapped by the surfaces orthogonal to the gradient of the effective dilaton field. The string dynamics has been shown to follow from an action functional subject to the Dirichlet boundary conditions. This way, we have succeeded in obtaining a macroscopic D-brane analogue.     

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density e μ gT⁴{\epsilon \propto gT^4} was on the order of n²/m_Pl²{n^2/m_{\rm Pl}^2} (in natural units), where n μ gT³{n \propto gT^3} is the fermion number density and g is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles (g ≈ 100), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about 10³² times smaller than its present value, giving ≈ 50 μm. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.     

Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas*

The electron-electron, electron-ion, ion-ion and charge-charge static structure factors are calculated for alkali (at T = 30 000 K, 60 000 K, n _e = 0.7 × 10²¹ ÷ 1.1 × 10²² cm^-3) and Be²⁺ (at T = 20 eV, n _e = 2.5 × 10²³ cm^-3) plasmas using the method described by Gregori et al. The dynamic structure factors for alkali plasmas are calculated at T = 30 000 K, n _e = 1.74 × 10²⁰, 1.11 × 10²² cm^-3 using the method of moments developed by Adamjan et al. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the repulsion due to the Pauli exclusion principle. The repulsive part of the Hellmann-Gurskii-Krasko (HGK) potential reflects important features of the ion structure. Our results on the static structure factors for Be²⁺ plasma deviate from the data obtained by Gregori et al., while our dynamic structure factors are in a reasonable agreement with those of Adamyan et al.: at higher values of k and with increasing k the curves damp down while at lower values of k, and especially at higher electron coupling, we observe sharp peaks also reported in the mentioned work. For lower electron coupling the dynamic structure factors of Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ do not differ while at higher electron coupling these curves split. As the number of shell electrons increases from Li⁺ to Cs⁺ the curves shift in the direction of low absolute value of ω and their heights diminish. We conclude that the short range forces, which we take into account by means of the HGK model potential, which deviates from the Coulomb and Deutsch ones, influence the static and dynamic structure factors significantly.