Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.Comment: 18 pages, MPA-AR-94-

Víctor Serge y la izquierda antiestalinista de New York

Atendiendo a la correspondencia entre Víctor Serge y la izquierda antiestalinista nortemericana, el autor sigue las intensas relaciones entre el escritor y militante ruso-belga y una serie de intelectuales norteamericanos. En los años que van desde los Juicios de Moscú hasta la Guerra Fría, el grupo de intelectuales neoyorquinos se encontraban en un proceso de profunda desradicalización, migrando desde el apoyo cuasi-trotskista al leninismo hacia la defensa de diversas formas de socialdemocracia. El pensamiento de Serge, por su parte, acusa recibo de las presiones anticomunistas propias de la Guerra Fría, intensificadas por los continuos horrores del estalinismo y la incapacidad del trotskismo para ofrecer una alternativa creíble. Sin embargo, aun cuando Serge se haya movido claramente hacia la derecha en sus últimos años, sus profundos lazos emocionales con la Revolución Rusa, su experiencia del leninismo y de la Oposición de Izquierda, eran lo suficientemente fuertes para impedir la total aceptación del anticomunismo vulgar que estaba devorando la vida intelectual en los Estados Unidos

Neutron Stars in f(R) Gravity with Perturbative Constraints

We study the structure of neutron stars in f(R) gravity theories with perturbative constraints. We derive the modified Tolman-Oppenheimer-Volkov equations and solve them for a polytropic equation of state. We investigate the resulting modifications to the masses and radii of neutron stars and show that observations of surface phenomena alone cannot break the degeneracy between altering the theory of gravity versus choosing a different equation of state of neutron-star matter. On the other hand, observations of neutron-star cooling, which depends on the density of matter at the stellar interior, can place significant constraints on the parameters of the theory.Comment: Discussion extended, typos corrected, figures revised. Accepted for publication in PR

Yang-Mills Cosmologies and Collapsing Gravitational Sphalerons

Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the associated anomalous production of fermions. The Dirac equation is analyzed in these backgrounds. It is shown explicitly that a fermion energy level crosses from the negative to positive energy spectrum as the gauge field evolves between the topologically distinct vacua. The cosmological solutions are also generalized to include an axion field.Comment: 12 pages, harvmac, DAMTP93/R3

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

Existence of maximal hypersurfaces in some spherically symmetric spacetimes

We prove that the maximal development of any spherically symmetric spacetime with collisionless matter (obeying the Vlasov equation) or a massless scalar field (obeying the massless wave equation) and possessing a constant mean curvature $S^1 \times S^2$ Cauchy surface also contains a maximal Cauchy surface. Combining this with previous results establishes that the spacetime can be foliated by constant mean curvature Cauchy surfaces with the mean curvature taking on all real values, thereby showing that these spacetimes satisfy the closed-universe recollapse conjecture. A key element of the proof, of interest in itself, is a bound for the volume of any Cauchy surface $\Sigma$ in any spacetime satisfying the timelike convergence condition in terms of the volume and mean curvature of a fixed Cauchy surface $\Sigma_0$ and the maximal distance between $\Sigma$ and $\Sigma_0$. In particular, this shows that any globally hyperbolic spacetime having a finite lifetime and obeying the timelike-convergence condition cannot attain an arbitrarily large spatial volume.Comment: 8 pages, REVTeX 3.

Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.Comment: 13 pages LaTe

Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound

In many cases a nonlinear scalar field with potential $V$ can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for homogeneous spacetimes. It is shown that, under the assumption that $V$ has a strictly positive minimum, Wald's theorem on spacetimes with positive cosmological constant can be generalized to a wide class of potentials. In some cases detailed information on late-time asymptotics is obtained. Results on the behaviour in the past time direction are also presented.Comment: 16 page

Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.Comment: 30 pages, many postscript figure