Noether symmetries of Bianchi type I spacetimes via Rif tree approach

In this paper, we have studied Noether symmetries of the general Bianchi type I spacetimes. The Lagrangian associated with the most general Bianchi type I metric is used to find the set of Noether symmetry equations. These equations are analyzed using an algorithm, developed in Maple, to get all possible Bianchi type I metrics admitting different Noether symmetries. The set of Noether symmetry equations is then solved for each metric to obtain the Noether symmetry algebras of dimensions 4, 5, 6 and 9.

Classical and quantum cosmology in f(T)-gravity theory: A Noether symmetry approach

In the framework of [Formula: see text]-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of [Formula: see text] is determined. A point transformation in the 2D augmented space restricts one of the variables to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly, for quantum cosmology, the WD equation is constructed and a possible solution has been evaluated.

Multi-scalar field cosmological model and possible solutions using Noether symmetry approach

In this work, a cosmological model is considered having two scalar fields minimally coupled to gravity with a mixed kinetic term. The model is characterized by the coupling function and the potential function which are assumed to depend on one of the scalar fields. Instead of choosing these functions phenomenologically here, they are evaluated assuming the existence of Noether symmetry. By appropriate choice of a point transformation in the augmented space, one of the variables in the Lagrangian becomes cyclic and the evolution equations become much simpler to have solutions. Finally, the solutions are analyzed from cosmological view point.

Approximate Mei Symmetries and Invariants of the Hamiltonian

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.

The (2+1) dimensional metric f (R) gravity non-minimally coupled with fermion field

In this article, we examine a gravitational theory including a fermion field that is non-minimally coupled to metric f (R) gravity in (2+1) dimensions. We give the field equations for fermion fields and Friedmann equations. In this context, we study cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

Noether symmetry approach in f (T, B) teleparallel gravity with a fermionic field

In this work, we consider a homogeneous and isotropic cosmological model of the universe in f (T, B) gravity with non-minimally coupled fermionic field. In order to find the form of the coupling function F(Ψ), the potential function V (Ψ) of the fermionic field and the function f (T, B), we found through the Noether symmetry approach. The results obtain are coincide with the observational data that describe the late-time accelerated expansion of the universe.

New static cylindrical symmetric solutions in GR for unfamiliar EoS parameter values via Noether symmetry

The solutions for the field equations of f(R) gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the $$f(R)=f_0 R$$ f ( R ) = f 0 R case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non-dust matter.

Stellar structures admitting Noether symmetries in f(ℛ,𝒯 ) gravity

This paper investigates the geometry of compact stellar objects via Noether symmetry strategy in the framework of curvature-matter coupled gravity. For this purpose, we assume the specific model of this theory to evaluate Noether equations, symmetry generators and corresponding conserved parameters. We use conserved parameters to examine some fascinating attributes of the compact objects for suitable values of the model parameters. It is analyzed that compact objects in this theory depend on the conserved quantities and model parameters. We find that the obtained solutions provide the viability of this process as they are compatible with the astrophysical data.