J. Mark Heinzle

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We investigate the dynamics of spatially homogeneous solutions of the EinsteinVlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the past there exists a singularity. We identify and describe all possible past asymptotic states; in particular, on the past(More)
We study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a bounded state space. Based on a dynamical systems analysis we derive(More)
We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a region with compact closure. Based on a dynamical systems analysis we derive theorems that guarantee that the(More)
We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a 3-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two(More)
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded plus half-advanced solution of the scalar wave equation, we consider an N-body problem: We investigate configurations of N particles which form an equilateral N angle and are in helical motion about their common center. We prove that there exists a(More)
The dimensional reduction of D-dimensional spacetimes arising in string/M-theory, to the conformal Einstein frame, may give rise to cosmologies with accelerated expansion. Through a complete analysis of the dynamics of doubly warped product spacetimes, in terms of scale invariant variables, it is demonstrated that for D ≥ 10, eternally accelerating(More)