The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure

Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.Comment: 31 pages, 4 figure

A unified treatment of cubic invariants at fixed and arbitrary energy

Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the invariant generally corresponds to a third rank Killing tensor, whose existence at a fixed energy value forces the metric to satisfy a nonlinear integrability condition expressed in terms of a Kahler potential. Further conditions, leading to a system of equations which is overdetermined except for singular cases, are added when the energy is arbitrary. As solutions to these equations we obtain several new superintegrable cases in addition to the previously known cases. We also discover a superintegrable case where the cubic invariant is of a new type which can be represented by an energy dependent linear invariant. A complete list of all known systems which admit a cubic invariant at arbitrary energy is given.Comment: 16 pages, LaTeX2e, slightly revised version. To appear in J. Math. Phys. vol 41, pp 370-384 (2000

Closed cosmologies with a perfect fluid and a scalar field

Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final singularity (for all values of the potential parameter kappa), or else they expand forever towards a flat power-law inflationary solution (when kappa^2<2). As an illustration of the intermediate dynamical behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic fluid, and of a massless scalar field in detail. We also briefly discuss Bianchi type IX models.Comment: 15 pages, 10 figure

Lax pair tensors in arbitrary dimensions

A recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and coupling-constant metamorphosis to obtain a geometric Lax formulation. We also exploit the results to construct integrable spacetimes, satisfying the weak energy condition.Comment: 8 pages, uses IOP style files. Minor correction. Submitted to J. Phys

Spatially self-similar spherically symmetric perfect-fluid models

Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.Comment: 21 pages, 6 eps-figure

Matrix Degradation in Human Immunodeficiency Virus Type 1-Associated Tuberculosis and Tuberculosis Immune Reconstitution Inflammatory Syndrome: A Prospective Observational Study.

Background: Extensive immunopathology occurs in human immunodeficiency virus (HIV)/tuberculosis (TB) coinfection, but the underlying molecular mechanisms are not well-defined. Excessive matrix metalloproteinase (MMP) activity is emerging as a key process but has not been systematically studied in HIV-associated TB. Methods: We performed a cross-sectional study of matrix turnover in HIV type 1 (HIV-1)-infected and -uninfected TB patients and controls, and a prospective cohort study of HIV-1-infected TB patients at risk of TB immune reconstitution inflammatory syndrome (TB-IRIS), in Cape Town, South Africa. Sputum and plasma MMP concentrations were quantified by Luminex, plasma procollagen III N-terminal propeptide (PIIINP) by enzyme-linked immunosorbent assay, and urinary lipoarabinomannan (LAM) by Alere Determine TB LAM assay. Peripheral blood mononuclear cells from healthy donors were cultured with Mycobacterium tuberculosis and extracellular matrix in a 3D model of TB granuloma formation. Results: MMP activity differed between HIV-1-infected and -uninfected TB patients and corresponded with specific TB clinical phenotypes. HIV-1-infected TB patients had reduced pulmonary MMP concentrations, associated with reduced cavitation, but increased plasma PIIINP, compared to HIV-1-uninfected TB patients. Elevated extrapulmonary extracellular matrix turnover was associated with TB-IRIS, both before and during TB-IRIS onset. The predominant collagenase was MMP-8, which was likely neutrophil derived and M. tuberculosis-antigen driven. Mycobacterium tuberculosis-induced matrix degradation was suppressed by the MMP inhibitor doxycycline in vitro. Conclusions: MMP activity in TB differs by HIV-1 status and compartment, and releases matrix degradation products. Matrix turnover in HIV-1-infected patients is increased before and during TB-IRIS, informing novel diagnostic strategies. MMP inhibition is a potential host-directed therapy strategy for prevention and treatment of TB-IRIS