J. Mark Heinzle

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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)
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 the dynamics of spatially homogeneous solutions of the Einstein-Vlasov 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(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 relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of(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)
For spherically symmetric relativistic perfect fluid models, the well-known Buchdahl inequality provides the bound 2M/R 8/9, where R denotes the surface radius and M the total mass of a solution. By assuming that the ratio p/ρ be bounded, where p is the pressure, ρ the density of solutions, we prove a sharper inequality of the same type, which depends on(More)
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