1,675 research outputs found
Quantization of Midisuperspace Models
We give a comprehensive review of the quantization of midisuperspace models.
Though the main focus of the paper is on quantum aspects, we also provide an
introduction to several classical points related to the definition of these
models. We cover some important issues, in particular, the use of the principle
of symmetric criticality as a very useful tool to obtain the required
Hamiltonian formulations. Two main types of reductions are discussed: those
involving metrics with two Killing vector fields and spherically symmetric
models. We also review the more general models obtained by coupling matter
fields to these systems. Throughout the paper we give separate discussions for
standard quantizations using geometrodynamical variables and those relying on
loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit
Exact solutions and their interpretation
This is the account of the workshop Exact solutions and their interpretation
at the 16-th International Conference on General Relativity and Gravitation
held in Durban, July 15-21, 2001. Work reported in 32 oral contributions
spanned a wide variety of topics, ranging from exact radiative spacetimes to
cosmological solutions. Two invited review talks, on the role of exact
solutions in string theory and in cosmology, are also described.Comment: 18 pages. To be published in: Proceedings of the 16th International
Conference on General Relativity and Gravitation, Durban, 15 - 21 July, 2001,
eds. N.T. Bishop and S.D. Maharaj, World Scientifi
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps--closely related to Poincare
maps--that describe chaotic interactions between colliding solitary waves. The
chaotic behavior of such solitary wave collisions depends on the transfer of
energy to a secondary mode of oscillation, often an internal mode of the pulse.
Unlike previous analyses, this map allows one to understand the interactions in
the case when this mode is excited prior to the first collision. The map is
derived using Melnikov integrals and matched asymptotic expansions and
generalizes a ``multi-pulse'' Melnikov integral and allows one to find not only
multipulse heteroclinic orbits, but exotic periodic orbits. The family of maps
derived exhibits singular behavior, including regions of infinite winding. This
problem is shown to be a singular version of the conservative Ikeda map from
laser physics and connections are made with problems from celestial mechanics
and fluid mechanics.Comment: 29 pages, 17 figures, submitted to Chaos, higher-resolution figures
available at author's website: http://m.njit.edu/goodman/publication
Scaling Cosmologies of N=8 Gauged Supergravity
We construct exact cosmological scaling solutions in N=8 gauged supergravity.
We restrict to solutions for which the scalar fields trace out geodesic curves
on the scalar manifold. Under these restrictions it is shown that the axionic
scalars are necessarily constant. The potential is then a sum of exponentials
and has a very specific form that allows for scaling solutions. The scaling
solutions describe eternal accelerating and decelerating power-law universes,
which are all unstable. An uplift of the solutions to 11-dimensional
supergravity is carried out and the resulting timedependent geometries are
discussed. In the discussion we briefly comment on the fact that N=2 gauged
supergravity allows stable scaling solutions.Comment: 17 pages; referenced added, reportnr changed and some corrections in
section
Supersymmetric Homogeneous Quantum Cosmologies Coupled to a Scalar Field
Recent work on supersymmetric Bianchi type IX cosmologies coupled to a
scalar field is extended to a general treatment of homogeneous quantum
cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types
I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the
Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the
earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX,
describing a virtual wormhole fluctuation, an additional explicit solution is
given and identified with the `no-boundary state'.Comment: 23 PAGE
Resonant Geometric Phases for Soliton Equations
The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons
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