Related papers: Noether symmetries in Bianchi universes
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present…
Einstein gravity minimally coupled to a self-interacting scalar field is investigated in the static and isotropic situation. We explicitly construct in partially closed form a new black-hole solution with exponentially decaying scalar hair.…
In this paper, we consider a gravitational theory including a Dirac field that is non-minimal coupled to gravity in $2+1$ dimensions. Noether gauge symmetry approach can be used to fix the form of coupling function $F(\Psi)$ and the…
The cosmological singularities of the Bianchi I universe are analyzed in the setting of loop geometry underlying the loop quantum cosmology. We solve the Hamiltonian constraint of the theory and find the Lie algebra of elementary…
We investigate Bianchi I cosmological model in the theory of a dilatonM field coupled to gravity through a Gauss-Bonnet term. Two type ofM cosmological singularity are distinguished. The former is analogous toM the Einstein gravity…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
We consider minisuperspace models constituted of Bianchi I geometries with a free massless scalar field. The classical solutions are always singular (with the trivial exception of flat space-time), and always anisotropic once they begin…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
We consider a system of interacting spinor and scalar fields in a gravitational field given by a Bianchi type-I cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative…
We prove a theorem concerning the Noether symmetries for the area minimizing Lagrangian under the constraint of a constant volume in an n-dimensional Riemannian space. We illustrate the application of the theorem by a number of examples.
The present study reexamines the recent work of Pradhan et al. (Indian J. Phys. 88: 757, 2014) and obtained general exact solutions of the Einstein's field equations with variable gravitational and cosmological "constants" for a spatially…
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in…
In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar…
We consider a cosmological model in a Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas defined in Weyl Integrable gravity. In the Einstein-Weyl theory a scalar field is introduced in a geometric way.…
We revisit the static spherically symmetric solutions of Einstein's General Relativity with a conformally coupled scalar field in arbitrary dimensions. Using a four rank tensor introduced earlier we recast the field equations in a…