Cosmological models with fluid matter undergoing velocity diffusion

A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a cosmological scalar field term is added to the left hand side of the Einstein equations. This hypothesis promotes diffusion to a new mechanism for accelerated expansion in cosmology. It is shown that diffusion alters not only quantitatively, but also qualitatively the global dynamical properties of the standard cosmological models.     

Analytic solutions in the dyon black hole with a cosmic string: Scalar fields,Hawking radiation and energy flux

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.     

Spéculation sur la cosmologie quantique primordiale

An old-fashioned axiomatic formalism for the quantization of the gravitational field is adapted to a recently introduced notion of cosmological gravitational wave. Dynamical equations for the quantum field are proposed. An outline for the primordial cosmological scenario is suggested.

     

Singularity formation in general relativistic dynamics of homogeneous scalar fields

Collapsing dynamics of a wide class of self-interacting, self-gravitating homogeneous scalar field models is analyzed. The assumptions made on the potential satisfy some general conditions allowing to show that the generic evolution is divergent in a finite time. Combining results shown here with the ones from [R. Giambó, F. Giannoni, G. Magli, J. Math. Phys. 49 (2008) 042504], dealing with sub-exponential growing potentials, allows us to obtain the same results of singularity formation for more general potentials. Moreover it turns out that these models can be completed to find radiating collapsing star models of the Vaidya type, where blackholes are generically formed.     

Confluent Heun functions and the physics of black holes: Resonant frequencies,Hawking radiation and scattering of scalar waves

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.     

Free particle in q-deformed configuration space

The SO _q (N)-invariant Schrödinger equation for the free particle is formulated in polar coordinates as a partial differential equation in noncommutative geometry. For each value of the total angular momentum, a Hilbert space of radial functions is constructed as the space of normalizable functions respective to the q-integral. The spectrum of the Hamiltonian is found to be discrete.     

Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Killing spinor initial data sets

A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space-spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to the twistor and/or Killing equations. These lead to the notions of twistor and Killing spinor initial data. These notions are used to obtain a characterisation of initial data sets whose developments are of Petrov type N or D.     

An equivalence theorem for string solutions of the Einstein matter-gauge equations

String-like static solutions of the Einstein matter-gauge equations have interesting implications in cosmology. It has been shown recently that, at a critical coupling phase, this system of equations allows a reduction into a coupled Einstein-Bogomol'nyi system. In this Letter, we prove that, in the important case where the underlying two-dimensional Riemannian manifold is either compact or asymptotically Euclidean, the two systems are actually equivalent. Moreover, we show that the standard assumption that the strings reside in a conformally Euclidean surface will give us a metric which fails to be asymptotically Euclidean. In particular, in the radially symmetric case, we establish under the finite energy condition the boundary behavior of the metric. These results may indicate that a string solution will inevitably lead to nonflatness of the space at infinity even on the cross-section.     

Decomposition of the Fock Space in Two-Dimensional Square Lattice Systems

We discuss how to decompose the Fock space of a many-fermion system embedded in two-dimensional square lattice. Wefirst notice that the symmetry group inherent in the system is one of the two-dimensional space groups. We shortly review thecorresponding irreducible representations of the group. We then find the characters of the reducible representation of the many-fermion Fock space. Using the characters, we obtain the multiplicity of each irreducible representation contained in the Fock space of a fixed number of fermions. We present specific examples, where we calculate the multiplicities which are the dimensions of the decomposed spaces.     

Symmetries of the Einstein Hamiltonian

The vacuum Einstein equations for metrics that have two commuting spacelike Killing vector fields are studied from a Hamiltonian point of view using the Ashtekar variables. It is shown that the evolution equations are equivalent to those of a modified SL(2) principal chiral model with a time dependent coupling constant. This fact is used to extract an infinite set of symmetries of the Einstein Hamiltonian via a generalized zero-curvature formulation. These symmetries give evolving observables explicitly on the phase space, and may be viewed as providing an infinite set of solutions of the Hamiltonian Einstein equations. The possibility of quantization using these observables is briefly discussed.     

Matching stationary spacetimes

Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary time-like hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.     

The Bohm-Aharonov effect: A seven-dimensional structural group

We realize a nonfaithful representation of a seven-dimensional Lie algebra, the extension of which to its universal enveloping algebra contains most of the observables of the scattering Aharonov-Bohm effect, as essentially self-adjoint operators: the scattering Hamiltonian, the total and kinetic angular momenta, the positions and the kinetic momenta. By restriction, we obtain the model introduced in Lett. Math. Phys. 1 (1976), 155–163.     

Towards a generalized distribution formalism for gauge quantum fields

We prove that the distributions defined on the Gelfand-Shilov spacesS with < 1 and, hence, more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic technique suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proof covering the most general and difficult case = 0 is based on the use of the theory of plurisubharmonic functions and Hörmander'sL ²-estimates.This work was supported in part by a Soros Humanitarian Foundation Grant awarded by the American Physical Society.     

Induced classical gravity

We review the induced-gravity approach according to which the Einstein gravity is a long-wavelength effect induced by underlying fundamental quantum fields due to the dynamical-scale symmetry breaking. It is shown that no ambiguities arise in the definition of the induced Newton and cosmological constants if one works with the path integral for fundamental fields in the low-scale region. The main accent is on a specification of the path integral which enables us to utilize the unitarity condition and thereby avoid ambiguities. Induced Einstein equations appear from the symmetry condition that the path integral of fundamental fields for a slowly varying metric is invariant under the local GL(4, R)-transformations of a tetrad, which contain the local Euclidean Lorentz, O(4)-rotations as a subgroup. The relationship to induced quantum gravity is briefly outlined.     

Singularities with C 0 metrics

We find that Green's functions for two C ⁰ metrics are not of the Hadamard form.     

Sum rules for multi-photon spectroscopy of ions in finite symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity-forbiddenp-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.     

Algebras in higher-dimensional statistical mechanics - the exceptional partition (mean field) algebras

We determine the structure of the partition algebraP _n(Q) (a generalized Temperley-Lieb algebra) for specific values ofQ , focusing on the quotient which gives rise to the partition function ofn siteQ-state Potts models (in the continuousQ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is nonsemisimple iffQ is a nonnegative integer less than 2n-1. We determine the dimension of the key irreducible representation in every specialization.Work supported by the Packard Foundation.     

The hopf algebra of vector fields on complex quantum groups

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A _n , B _n , C _n , and D _n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.Humboldt Fellow.