General Relativity and Quantum Cosmology (gr-qc)

Abstract: Taking the Noether gauge symmetry approach into account, we find spherically symmetric static black hole solutions of the non-minimal gauge-gravity Lagrangian of the $\mathcal{R}^\beta F^2$ model. At first, we consider a system of differential equations for the general non-minimal couplings of $Y(\mathcal{R})F^2$ type, and then, we regard a particular $\mathcal{R}^\beta F^2$ non-minimal model to find the exact black hole solution and analyze its symmetries. As the next step, we calculate the thermodynamical quantities of the black hole and study its interesting behavior. Besides, we address thermal stability and examine the possibility of the van der Waals-like phase transition.

Abstract: Inspired by some Lorentzian versions of the notion of metric and length space introduced by Kunzinger and S\"amman, and more recently, by M\"uller, and Minguzzi and S\"uhr, we construct the c-completion of these models by previously discussing the notion of Lorentzian metric space. We not only prove that this construction is applicable to very general Lorentzian metric spaces, including spacetimes of low regularity, but also endow the c-completion with a structure of Lorentzian metric space by itself. We also prove that the c-completion constitutes a well-suited extension of the original space, which is sensible to certain causal properties of that space.

Abstract: In the framework of the Einstein-Dirac-aether theory we consider a phenomenological model of the spontaneous growth of the fermion number, which is triggered by the dynamic aether. The trigger version of spinorization of the early Universe is associated with two mechanisms: the first one is the aetheric regulation of behavior of the spinor field; the second mechanism can be related to a self-similarity of internal interactions in the spinor field. The dynamic aether is designed to switch on and switch off the self-similar mechanism of the spinor field evolution; from the mathematical point of view, the key of such a guidance is made of the scalar of expansion of the aether flow, proportional to the Hubble function in the isotropic cosmological model. Two phenomenological parameters of the presented model are shown to be considered as factors predetermining the total number of fermions born in the early Universe.

Abstract: We are interested in the charged dust solutions of the Einstein field equations in stationary and axially symmetric spacetimes; and inquire if the naked singularities of the Israel-Wilson-Perjes (IWP) metrics can be removed. The answer is negative in four dimensions. We examine whether this negative result can be avoided by adding scalar or dilaton fields. We show that IWP metrics also arise as solutions of the Einstein-Maxwell system with a stealth dilaton field. We determine the IWP metrics completely in terms of one complex function satisfying the Laplace equation. With the inclusion of the stealth dilaton field, it is now possible to add a perfect fluid source. In this case the field equations reduce to a complex cubic equation. Hence this procedure provides interior solutions to each IWP metric; and it is possible to cover all naked singularities inside a compact surface where there is matter distribution.

Abstract: We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady states of the Einstein-Vlasov system and their stability properties. In order to put things into perspective we include the Vlasov-Poisson system and the relativistic Vlasov-Poisson system into the discussion.