The Creation of the Universe as a Quantum Phenomenon

All solutions of Einstein's equations for pressure‐free matter which exhibit local rotational symmetry were classified in an earlier paper by one of us. This paper extends the earlier theory to the case of a general fluid, with an electromagnetic field possibly present. A classification of these solutions for a perfect fluid is given, and assuming a physically reasonable equation of state, some exact solutions of cosmological interest are obtained. Finally, the difficulties encountered when extending the treatment to a general fluid are discussed; the same general classification can be made.

Solutions of Einstein's equations for a fluid which exhibit local rotational symmetry

The research on viscous cosmological models is reviewed and carried further Inflationary cosmological models of Bianchi type-I with shear, bulk, and nonlinear viscosity are studied The inflation field energy is represented by a two-components cosmic fluid consisting of a vacuum fluid and a Zel'dovich fluid It is shown that there exist models in which the viscous Zel'dovich fluid removes the initial singularity of the corresponding viscosity free models The mean expansion of a Zel'dovich dominated unvierse is found to be independent of shear viscosity and anisotropy Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy

Viscous Inflationary Universe Models

Linear maps of matrices describing the evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is not positive, unless we restrict the domain on which the map acts. Nevertheless, their form is similar to that of completely positive maps. Only some minus signs are inserted in the operator-sum representation. Each map is the difference of two completely positive maps. The maps are first obtained as maps of mean values and then as maps of basis matrices. These forms also prove to be useful. An example for two entangled qubits is worked out in detail. The relation to earlier work is discussed.

Dynamics of initially entangled open quantum systems

Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field generated by the companion, with a constant response coefficient. However, if the orbital motion approaches a resonance with one of the internal modes of the neutron star, this adiabatic description of tidal effects starts to break down, and the tides become dynamical. In this paper, we consider dynamical tides in general relativity due to the quadrupolar fundamental oscillation mode of a neutron star. We devise a description of the effects of the neutron star's finite size on the orbital dynamics based on an effective point-particle action augmented by dynamical quadrupolar degrees of freedom. We analyze the post-Newtonian and test-particle approximations of this model and incorporate the results into an effective-one-body Hamiltonian. This enables us to extend the description of dynamical tides over the entire inspiral. We demonstrate that dynamical tides give a significant enhancement of matter effects compared to adiabatic tides, at least for neutron stars with large radii and for low mass-ratio systems, and should therefore be included in accurate models for gravitational-wave data analysis.

Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian

Einstein's field equations for a homogeneous isotropic universe are written in terms of a conformally flat coordinate system for both the closed and the open cases. It is shown that these can be readily integrated for equations of state of the form p = aρ in terms of algebraic functions. Explicit solutions and expressions for the radius and Hubble factor are given for a = 1, ⅓, and for p = 0.

Expanding universe in conformally flat coordinates.

From SU(3) to gravity

A canonical formalism for spinning particles suitable for the formulations of a general relativistic covariant statistical mechanics of particles endowed with spin is developed. For that purpose the bracket for internal and external variables is given. In particular, limiting consideration to the spin tensor S/sup ..mu..v/, it has been possible to define momenta that are the true conjugates to the position variables. For the case considered the Hamiltonian function in addition to the invariant mass involves only one additional scalar. The equations of motion are then found by calculating the brackets of the dynamical variables with that Hamiltonian, and are compared to those obtained by other methods. The conjugate variables in the internal space that has to be adjoined to the (eight-dimensional) phase space for a complete covariant description of spinning particles are also given.

Canonical formalism and equations of motion for a spinning particle in general relativity

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists an N-dimensional linear vector space with N≥5. This space is decomposed into a four-dimensional tangent space and an (N - 4)-dimensional internal space. On the basis of geometric considerations, one arrives at a number of fields, the field equations being derived from a variational principle. Among the fields obtained there are the electromagnetic field, Yang-Mills gauge fields, and fields that can be interpreted as describing matter. As a simple example, the case N=6 is considered.

A geometric foundation for a unified field theory

Conformally flat line-elements are applied to imperfect fluids in cosmology. Explicit solutions of the field equations are given for an equation of state for which the pressure is proportional to the density. Both the isotropic case (for which the shear viscosity vanishes) and the non-isotropic case are considered and expressions derived for the appropriate coefficients of shear and bulk viscosity, as well as density.

Gerald E. Tauber

Papers

Expanding universe in conformally flat coordinates.

From SU(3) to gravity

Canonical formalism and equations of motion for a spinning particle in general relativity

A geometric foundation for a unified field theory

Expanding Universe with Bulk and Shear Viscosity in Conformally Flat Coordinates