We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4D phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3D sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H 0 is negative. If H 0 is positive the trajectories end up in a curvature singularity that can be, depending on initial conditions, isotropic or anisotropic. In particular, if the initial magnetic field intensity is sufficiently large the collapsing singularity will always be anisotropic and pointing in the same direction of the field.

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I spacetime with a Kasner-like metric. We examine the dynamics of this system by means of a qualitative and numerical study of EinsteinMaxwell field equations which reduce to a non-linear autonomous system. For all initial conditions and combinations of free parameters the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the "cigar" or "plate" types.

Abstract:We examine the dynamics of a self-gravitating magnetized neutron gas as a source of a Bianchi I spacetime described by the Kasner metric. The set of EinsteinMaxwell field equations can be expressed as a dynamical system in a 4-dimensional phase space. Numerical solutions of this system reveal the emergence of a point-like singularity as the final evolution state for a large class of physically motivated initial conditions. Besides the theoretical interest of studying this source in a fully general relativistic context, the resulting idealized model could be helpful in understanding the collapse of local volume elements of a neutron gas in the critical conditions that would prevail in the center of a compact object.

Abstract. We examine the dynamics of a self-gravitating magnetized electron gas at finite temperature near the collapsing singularity of a Bianchi-I spacetime. Considering a general and appropriate and physically motivated initial conditions, we transform Einstein-Maxwell field equations into a complete and self-consistent dynamical system amenable for numerical work. The resulting numerical solutions reveal the gas collapsing into both, isotropic ("point-like") and anisotropic ("cigar-like") singularities, depending on the initial intensity of the magnetic field. We provide a thorough study of the near collapse behavior and interplay of all relevant state and kinematic variables: temperature, expansion scalar, shear scalar, magnetic field, magnetization and energy density. A significant qualitative difference in the behavior of the gas emerges in the temperature range T ∼ 10 4 K and T ∼ 10 7 K.