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Register a new userGeneralized Kantowski-Sachs type spacetime metrics and their harmonicity
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Added by
Murat Altunba\\c{s}
Publication date
2021
fields
Physics
and research's language is
English
Authors
Murat Altunbac{s}
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In this paper, we deal with harmonic metrics with respect to generalized Kantowski-Sachs type spacetime metrics. We also consider the Sasaki, horizontal and complete lifts of generalized Kantowski-Sachs type spacetime metrics to tangent bundle and study their harmonicity.
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Scalar field cosmologies with a generalized harmonic potential and matter with energy density $rho_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(gamma-1)rho_m, ; gammain[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lema^itre--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged systems are two anisotropic contracting solutions, which are non--flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $0leq gamma leq 2$, and flat FLRW matter--dominated universe if $0leq gamma leq frac{2}{3}$. For closed FLRW metric late--time attractors of full and averaged systems are a flat matter--dominated FLRW universe for $0leq gamma leq frac{2}{3}$ as in KS and Einstein-de Sitter solution for $0leqgamma<1$. Therefore, time--averaged system determines future asymptotics of full system. Also, oscillations entering the system through Klein-Gordon (KG) equation can be controlled and smoothed out when $D$ goes monotonically to zero, and incidentally for the whole $D$-range for KS and for closed FLRW (if $0leq gamma< 1$) too. However, for $gammageq 1$ closed FLRW solutions of the full system depart from the solutions of the averaged system as $D$ is large. Our results are supported by numerical simulations.
We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of this Lie group on the space of generalized metrics. As an application, we show that the moduli space of generalized metrics is stratified by ILH submanifolds and relate it to the moduli space of usual metrics. Finally, we extend these results to odd exact Courant algebroids.
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of the integrability condition for generalized contact structures; (3) in light of new results on multiplicative forms and Spencer operators, it allows a simple interpretation of the defining equations of a generalized contact structure in terms of Lie algebroids and Lie groupoids.
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to $C^{1,1}$. Our approach is based on regularisations of the metric adapted to the causal structure.
We investigate Kantowski-Sachs models in Einstein-{ae}ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A. A. Coley, G. Leon, P. Sandin and J. Latta (JCAP 12, 010, 2015), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. In particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.
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