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Register a new userDynamics of a self-gravitating neutron source
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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 Einstein-Maxwell 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.
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The dynamics of a self-gravitating neutron gas in presence of a magnetic field is being studied taking the equation of state of a magnetized neutron gas obtained in a previous study [2]. We work in a Bianchi I spacetime characterized by a Kasner metric, this metric allow us to take into account the anisotropy that introduces the magnetic field. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We get numerical solutions of the system. In particular there is a unique point like solution for different initial conditions. Physically this singular solution may be associated with the collapse of a local volume of neutron material within a neutron star.
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 4-dimensional 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 3-dimensional 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, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular point) or anisotropic (singular line). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the line points in the same direction of the field.
We address the question whether a medium featuring $p + rho = 0$, dubbed $Lambda$- medium, has to be necessarily a cosmological constant. By using effective field theory, we show that this is not the case for a class of media comprising perfect fluids, solids and special super solids, providing an explicit construction. The low energy excitations are non trivial and lensing, the growth of large scale structures can be used to clearly distinguish $Lambda$-media from a cosmological constant.
We study the heat capacity of a static system of self-gravitating radiations analytically in the context of general relativity. To avoid the complexity due to a conical singularity at the center, we excise the central part and replace it with a regular spherically symmetric distribution of matters of which specifications we are not interested in. We assume that the mass inside the inner boundary and the locations of the inner and the outer boundaries are given. Then, we derive a formula relating the variations of physical parameters at the outer boundary with those at the inner boundary. Because there is only one free variation at the inner boundary, the variations at the outer boundary are related, which determines the heat capacity. To get an analytic form for the heat capacity, we use the thermodynamic identity $delta S_{rm rad} = beta delta M_{rm rad}$ additionally, which is derived from the variational relation of the entropy formula with the restriction that the mass inside the inner boundary does not change. Even if the radius of the inner boundary of the shell goes to zero, in the presence of a central conical singularity, the heat capacity does not go to the form of the regular sphere. An interesting discovery is that another legitimate temperature can be defined at the inner boundary which is different from the asymptotic one $beta^{-1}$.
We compute cosmological perturbations for a generic self-gravitating media described by four derivatively- coupled scalar fields. Depending on the internal symmetries of the action for the scalar fields, one can describe perfect fluids, superfluids, solids and supersolids media. Symmetries dictate both dynamical and thermodynamical properties of the media. Generically, scalar perturbations include, besides the gravitational potential, an additional non-adiabatic mode associated with the entropy per particle {sigma}. While perfect fluids and solids are adiabatic with {sigma} constant in time, superfluids and supersolids feature a non-trivial dynamics for {sigma}. Special classes of isentropic media with zero {sigma} can also be found. Tensor modes become massive for solids and supersolids. Such an effective approach can be used to give a very general and symmetry driven modelling of the dark sector.
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