Exact non-equilibrium solutions of the Einstein-Boltzmann equations

Includes bibliographical references.In this thesis we use the exact solution of the Boltzmann equation, with a relaxation-time model of collisions, to find solutions of the Einstein-Boltzmann system of equations. A covariant harmonic decomposition of the distribution function is used to obtain exact results. The conditions imposed by the conservation of particle number and energy-momentum, and by the H-theorem are determined. The properties of exact truncated Boltzmann solutions with first and second order anisotropies are investigated. Exact entropy results are obtained for the solution with first order anisotropy, and the solution with second order anisotropy is shown to obey exact thermodynamics laws. The Einstein-Boltzmann equations with relaxation-time model of collisions are solved in FRW and Bianchi I spacetime. In FRW spacetime, a general anisotropic solution and an isotropic solution are obtained. The non-equilibrium anisotropic solution with arbitrary isotropic relaxation function has vanishing particle flux and an equilibrium energy-momentum tensor. Specific forms of the relaxation function permit tilted solutions and solutions with non-zero bulk viscosity. Exact entropy results are derived for the isotropic solution showing that the H-theorem is satisfied. The non-equilibrium isotropic solution has vanishing non-equilibrium pressures and fluxes. The FRW and Bianchi I solutions are used to demonstrate the generation of anisotropy in FRW cosmologies. A relaxation length model of collisions is introduced. This model is used to obtain solutions of the Einstein-Boltzmann equations in static spherically symmetric spacetime. In this static model, anisotropic pressure comes from the bulk viscosity

Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II

We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.Comment: 16 pages LaTex, CQG documentstyle (ioplppt

Special Report on the State of HIV/AIDS in South Africa

It is axiomatic that the global fight against HIV/AIDS cannot be won without a decisive victory in South Africa, home to 20 percent of all people living with HIV/AIDS. So how is South Africa doing? And what is the likelihood it will meet the demand for essential prevention and treatment interventions by 2015? On Jan. 21 in Cape Town, Council on Foreign Relations Global Health Fellow Dr. Peter Navario convened a meeting of South Africa's foremost HIV/AIDS thinkers, policy-makers and practitioners to discuss the state of prevention and treatment at the epicenter of the pandemic. In this article, the experts weigh in on program gaps, the major challenges to achieving universal coverage of essential prevention and treatment interventions, and what it will take to surmount these challenges

Special Report on the State of HIV/AIDS in South Africa

It is axiomatic that the global fight against HIV/AIDS cannot be won without a decisive victory in South Africa, home to 20 percent of all people living with HIV/AIDS. So how is South Africa doing? And what is the likelihood it will meet the demand for essential prevention and treatment interventions by 2015? On Jan. 21 in Cape Town, Council on Foreign Relations Global Health Fellow Dr. Peter Navario convened a meeting of South Africa's foremost HIV/AIDS thinkers, policy-makers and practitioners to discuss the state of prevention and treatment at the epicenter of the pandemic. In this article, the experts weigh in on program gaps, the major challenges to achieving universal coverage of essential prevention and treatment interventions, and what it will take to surmount these challenges

Evidence from South Africa for a protracted end-Permian extinction on land

Earth’s largest biotic crisis occurred during the Permo–Triassic Transition (PTT). On land, this event witnessed a turnover from synapsid- to archosauromorph-dominated assemblages and a restructuring of terrestrial ecosystems. However, understanding extinction patterns has been limited by a lack of high-precision fossil occurrence data to resolve events on submillion-year timescales. We analyzed a unique database of 588 fossil tetrapod specimens from South Africa’s Karoo Basin, spanning ∼4 My, and 13 stratigraphic bin intervals averaging 300,000 y each. Using sample-standardized methods, we characterized faunal assemblage dynamics during the PTT. High regional extinction rates occurred through a protracted interval of ∼1 Ma, initially co-occurring with low origination rates. This resulted in declining diversity up to the acme of extinction near the Daptocephalus–Lystrosaurus declivis Assemblage Zone boundary. Regional origination rates increased abruptly above this boundary, co-occurring with high extinction rates to drive rapid turnover and an assemblage of short-lived species symptomatic of ecosystem instability. The “disaster taxon” Lystrosaurus shows a long-term trend of increasing abundance initiated in the latest Permian. Lystrosaurus comprised 54% of all specimens by the onset of mass extinction and 70% in the extinction aftermath. This early Lystrosaurus abundance suggests its expansion was facilitated by environmental changes rather than by ecological opportunity following the extinctions of other species as commonly assumed for disaster taxa. Our findings conservatively place the Karoo extinction interval closer in time, but not coeval with, the more rapid marine event and reveal key differences between the PTT extinctions on land and in the oceans