71 citations · 554 across the 28 of their papers we have counts for
24 papers · 1 filter
Spike statistics
J. Mark Heinzle, Claes Uggla
In this paper we explore stochastical and statistical properties of so-called recurring spike induced Kasner sequences. Such sequences arise in recurring spike formation, which is…
Spike Oscillations
J. Mark Heinzle, Claes Uggla, Woei Chet Lim
According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatia…
Constant mean curvature slicings of Kantowski-Sachs spacetimes
J. Mark Heinzle
We investigate existence, uniqueness, and the asymptotic properties of constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological consta…
The initial singularity of ultrastiff perfect fluid spacetimes without symmetries
J. Mark Heinzle, Patrik Sandin
We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of ex…
Oscillations toward the singularity of LRS Bianchi type IX cosmological models with Vlasov matter
Simone Calogero, J. Mark Heinzle
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent gala…
On closed cosmological models that satisfy the strong energy condition but do not recollapse
Simone Calogero, J. Mark Heinzle
We show the existence of a rather general class of closed cosmological models of Bianchi type IX that do not exhibit recollapse but expand for all times. This is despite the fact t…
Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
Simone Calogero, J. Mark Heinzle
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with…
Monotonic functions in Bianchi models: Why they exist and how to find them
J. Mark Heinzle, Claes Uggla
All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper…
A new proof of the Bianchi type IX attractor theorem
J. Mark Heinzle, Claes Uggla
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 attract…
Dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter
Simone Calogero, J. Mark Heinzle
We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of…
Bounds on 2m/r for static perfect fluids
J. Mark Heinzle
For spherically symmetric relativistic perfect fluid models, the well-known Buchdahl inequality provides the bound , where denotes the surface radius and th…
Asymptotics of LRS Bianchi type I cosmological models with elastic matter
Simone Calogero, J. Mark Heinzle
In this paper we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally di…
Dynamics of Bianchi type I elastic spacetimes
Simone Calogero, J. Mark Heinzle
We study the global dynamical behavior of spatially homogeneous solutions of the Einstein equations in Bianchi type I symmetry, where we use non-tilted elastic matter as an anisotr…
The cosmological billiard attractor
J. Mark Heinzle, Claes Uggla, Niklas Rohr
This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamenta…
Helically symmetric N-particle solutions in scalar gravity
Robert Beig, J. Mark Heinzle, Bernd G. Schmidt
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an…
Self-gravitating stationary spherically symmetric systems in relativistic galactic dynamics
Mikael Fjällborg, J. Mark Heinzle, Claes Uggla
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into…
Homoclinic chaos and energy condition violation
J. Mark Heinzle, N. Rohr, C. Uggla
In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where t…
Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
J. Mark Heinzle, Claes Uggla
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 fore…
Power-law Inflation in Spacetimes without Symmetry
J. Mark Heinzle, Alan D. Rendall
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…
CMC-Slicings of Kottler-Schwarzschild-de Sitter Cosmologies
Robert Beig, J. Mark Heinzle
There is constructed, for each member of a one-parameter family of cosmological models, which is obtained from the Kottler-Schwarzschild-de Sitter spacetime by identification under…
Matter and dynamics in closed cosmologies
J. Mark Heinzle, N. Rohr, C. Uggla
To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general ba…
Spherically symmetric relativistic stellar structures
J. Mark Heinzle, N. Rohr, C. Uggla
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 dyn…
(In)finiteness of Spherically Symmetric Static Perfect Fluids
J. Mark Heinzle
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the baro…
Remarks on the distributional Schwarzschild geometry
J. Mark Heinzle, Roland Steinbauer
This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum…