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- J. Mark Heinzle, Niklas Röhr, Claes Uggla
- 2008

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 3dimensional compact state space, thereby avoiding the non-regularity problems associated with the TolmanOppenheimer-Volkoff equation. The global picture of the… (More)

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of… (More)

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)

- Mikael Fjällborg, J. Mark Heinzle, Claes Uggla
- 2006

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)

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The ‘Bianchi type IX attractor theorem’ states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively… (More)

- Simone Calogero, J. Mark Heinzle
- SIAM J. Applied Dynamical Systems
- 2010

- Robert Beig, J Mark Heinzle, Bernd G Schmidt
- Physical review letters
- 2007

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)