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We discuss the relativistic kinetic theory for a simple, collisionless, charged gas propagating on an arbitrary curved spacetime geometry. Our general relativistic treatment is formulated on the tangent bundle of the spacetime manifold and takes advantage of its rich geometric structure. In particular, we point out the existence of a natural metric on the tangent bundle and illustrate its role for the development of the relativistic kinetic theory. This metric, combined with the electromagnetic field of the spacetime, yields an appropriate symplectic form on the tangent bundle. The Liouville vector field arises as the Hamiltonian vector field of a natural Hamiltonian. The latter also defines natural energy surfaces, called mass shells, which turn out to be smooth Lorentzian submanifolds. A simple, collisionless, charged gas is described by a distribution function which is defined on the mass shell and satisfies the Liouville equation. Suitable fibre integrals of the distribution function define observable fields on the spacetime manifold, such as the current density and stress-energy tensor. Finally, the geometric setting of this work allows us to discuss the relationship between the symmetries of the electromagnetic field, those of the spacetime metric, and the symmetries of the distribution function. Taking advantage of these symmetries, we construct the most general solution of the Liouville equation an a Kerr-Newman black hole background. [ABSTRACT FROM AUTHOR]

We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincaré one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. Whenever the corresponding flow is restricted to special submanifolds of the tangent bundle, referred to as future mass shells, its projection onto the base manifold describes families of future-directed timelike geodesics. A collisionless simple gas is described by a distribution function on a particular mass shell, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy tensor. We show that the stress-energy tensor satisfies the familiar energy conditions and that both the current density and stress-energy tensor are divergence-free. Our discussion also includes the generalization to charged gases, a summary of the Einstein-Maxwell-Vlasov system in any dimensions, as well as a brief introduction to the general relativistic Boltzmann equation for a simple gas. [ABSTRACT FROM AUTHOR]

We discuss several properties of static, spherically symmetric wormholes with particular emphasis on the behavior of causal geodesics and the propagation of linear fields. We show there always exist null geodesics which are trapped in a region close to the throat. Depending upon the detailed structure of the wormhole geometry, these trapped geodesics can be stable, unlike the case of the Schwarzschild black hole. We also show that test scalar fields propagating on such wormholes are stable. However, when a mixture of ghost and Klein-Gordon scalar fields is used as a source of the Einstein equations we prove that the resulting static, spherically symmetric wormhole configurations are linearly unstable. [ABSTRACT FROM AUTHOR]

We study the Michel flow on a spherically symmetric black hole background for a polytropic equation of state. Based on standard tools from the theory of dynamical systems, we prove that for a polytropic index γ lying between 1 < γ ≤ 5/3 there exists a unique accretion flow for a given particle density number at infinity. This number can be matched to the density of the interstellar medium. [ABSTRACT FROM AUTHOR]

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of radial null geodesics. As an application we generate conformal diagrams for collapsing spherical dust clouds and analyze the causal structure of the resulting spacetimes. [ABSTRACT FROM AUTHOR]