Noether Symmetry Approach Research Articles

Non-local curvature gravity cosmology via Noether symmetries

We consider extensions of General Relativity based on the non-local function f(R,□−1R), where R is the Ricci curvature scalar and the non-locality is due to the term □−1R. We focus on cosmological minisuperspaces and select viable models by the Noether Symmetry Approach. Then we find viable exact solutions pointing out the role of non-locality in cosmology.

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.

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.

Dynamics of particle near time conformal slowly rotating Kerr black hole

In this work, we have developed the time conformal slowly rotating Kerr black hole using the approximate Noether symmetry approach. It is found that the slowly rotating Kerr black hole admits time conformal factor eεf(t), where ε is very small perturbation and f(t) is an arbitrary function of time. We have obtained the numerical solutions of geodesics for lowly rotating Kerr black hole and time conformal slowly rotating Kerr black hole. We have discussed the neutral and charged particle dynamics moving around time conformal slowly rotating Kerr black hole in the absence/presence of magnetic field. Moreover, we have analyzed graphically the behavior of effective force, effective potential and escape velocity of particles in the absence/presence of magnetic field near the event horizon. We have examined the conditions under which particle can escape from the surrounding of black hole after colliding with another particle. We have found the unstable orbits of particles near event horizon due to the effect of magnetic field and angular momentum.

Viable wormhole solutions in energy–momentum squared gravity

This paper investigates static wormhole solutions through Noether symmetry approach in the context of energy–momentum squared gravity. This newly developed proposal resolves the singularity of big bang and yields feasible cosmological results in the early times. We consider the particular model of this theory to establish symmetry generators and corresponding conserved quantities. For constant and variable red-shift functions, we examine the presence of viable traversable wormhole solutions for both dust and non-dust matter distributions and analyze the stable state of these solutions. We investigate the graphical interpretation of null and weak energy bounds for normal and effective energy–momentum tensors to examine the presence of physically viable wormhole geometry. It is found that realistic traversable and stable wormhole solutions are obtained for a particular model of this gravity.

Noether symmetries and quantum cosmology in extended teleparallel gravity

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt–Deser–Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.

Compact Stars Admitting Noether Symmetries in Energy-Momentum Squared Gravity

This paper investigates the geometry of compact stellar objects through the Noether symmetry approach in the energy-momentum squared gravity. This newly developed theory overcomes the problems of big bang singularity and provides the viable cosmological consequences in the early time universe. Moreover, its implications occur in high curvature regime where the deviations of energy-momentum squared gravity from general relativity is confirmed. We consider the minimal coupling model of this modified theory and formulate symmetry generators as well as corresponding conserved quantities. We use conservation relation and apply some suitable initial conditions to evaluate the metric potentials. Finally, we explore some interesting features of the compact objects for appropriate values of the model parameters through numeric analysis. It is found that compact stellar objects in this particular framework depend on the model parameters as well as conserved quantities. We conclude that Noether symmetries generate solutions that are consistent with the astrophysical observational data and hence confirm the viability of this procedure.

Three-dimensional black holes via Noether symmetries

We investigate the Noether symmetries of the Lagrangian for the stationary rotating BTZ-type three-dimensional spacetimes in $f(R)$ theory of gravity. A detailed analysis of Noether symmetries of (2+1)-dimensional rotating BTZ-type black hole spacetime model is presented. Applying the Noether symmetry approach, the first integrals (constants of motion) for each of Noether symmetries are obtained to look for the exact solutions. After solving the first integral equations depending on the form of the function $f(R)$, we derived some new (2+1)-dimensional rotating BTZ-type black hole solutions. We discussed the physical implications of the derived exact solutions. The thermodynamical properties of the obtained BTZ-type black hole solutions are analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of $r_{\pm}$, where $r_+$ is the event horizon and $r_{-}$ is the inner horizon. Further, it is shown that thermodynamic quantities obey the first law, and the Smarr-like formulas of the solutions we found are obtained.

Teleparallel gravity with non-minimally coupled f-essence via Noether symmetry approach

In this paper, we examine teleparallel gravity with non-minimally coupled with non-canonical fermionic fields (f-essence). Noether symmetry approach can be used to fix the forms of coupling F (Ψ) and the potential V (Ψ) functions of the fermionic fields. In the context of the Friedman-Robertson-Walker metric, we investigate cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

Noether symmetry approach in energy-momentum squared gravity

In this paper, we investigate the newly developed f(R, T 2) theory (R is the Ricci scalar and T 2 = T α β T α β , T α β demonstrates the energy-momentum tensor) to explore some viable cosmological models. For this purpose, we use the Noether symmetry approach in the context of flat Friedmann-Robertson-Walker (FRW) universe. We solve the Noether equations of this modified theory for two types of models and obtain the symmetry generators as well as corresponding conserved quantities. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the prospective models, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the Universe. In the first case, we take a special model of this theory and obtain new class of exact solutions with the help of conserved quantities. Secondly, we consider minimal and non-minimal coupling models of f(R, T 2) gravity. We conclude that conserved quantities are very useful to derive the exact solutions that are used to study the cosmic accelerated expansion.

Dark $$f(\mathcal{R},\varphi,\chi)$$ universe with Noether symmetry

Using the Noether symmetry approach, we investigate $$f( \mathcal{R} , \varphi ,\chi)$$ theories of gravity, where $$ \mathcal{R} $$ is the scalar curvature, $$ \varphi $$ is the scalar field, and $$\chi$$ is the kinetic term of $$ \varphi $$ . Based on the Lagrangian for $$f( \mathcal{R} , \varphi ,\chi)$$ gravity, we obtain the determining equations. We consider $$f( \mathcal{R} , \varphi ,\chi)$$ models of a flat Friedmann–Robertson–Walker universe. Using the obtained solutions, we find conserved quantities. In the framework of this scenario, the continuity equation is extremely important for analyzing the energy density and pressure. Using the first integral of motion, we present a graphical analysis of the energy density, pressure component, and parameter of the equation of state. The negativity of the pressure observed in the considered cases in fact suggests that this theory can describe a Noether universe with dark matter.

Non-local curvature and Gauss\u2013Bonnet cosmologies by Noether symmetries

Non-local gravity cosmologies are considered under the standard of Noether symmetry approach. In particular, we focus on non-local theories whose gravitational actions depend on curvature and Gauss–Bonnet scalar invariants. Specific functional forms of the related point-like Lagrangians are selected by Noether symmetries, and we solve the corresponding field equations finding out exact cosmological solutions.

Noether symmetries of Einstein-aether scalar field cosmology

In this paper, we explore an Einstein-aether cosmological model by adding the scalar field in which it has an interaction with the aether field. For the cosmological implications of the model, we consider that the universe can be described by the spatially flat FRW metric together with the matter dominated universe. Applying Noether symmetry approach to the point-like Lagrangian we determine the explicit forms of unknown functions i.e. the potential and coupling function. We solve the analytical cosmological solutions of the field equations admitting the Noether symmetry, basically divided into two parts. Our results show that the obtained solutions lead to an accelerated expansion of the universe. We also discuss the tensor perturbations within the framework of this model in order to get information about the mass of gravitational waves.

Interacting phantom cosmology via Noether symmetry approach

In this paper, we have presented a cosmological model where a phantom scalar field is minimally coupled to dark matter component. Noether symmetry method was applied both to investigate the cosmological solution and to find out what is the form of the potential of scalar field and the unknown function in the considered model. By using this method, these forms are resulted as trigonometric functions. Also, the obtained cosmological solutions are compatible with observations describing the accelerated expansion of the Universe. Furthermore, it turns out that the effective equation of state parameter in the model can cross the phantom divide line.

Noether symmetries of LRS Bianchi type-I spacetime in f(ℛ,φ,χ) gravity

This paper investigates the Noether symmetry approach in modified [Formula: see text] theory of gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is a scalar field and [Formula: see text] is the kinetic energy term. For this purpose, we consider Locally Rotationally Symmetric (LRS) Bianchi Type-I spacetimes. The cosmological solutions are developed through Noether symmetry approach. The determining equations are computed in the context of a point-like Lagrangian for [Formula: see text] gravity. In particular, three different cases are taken into account for the LRS Bianchi Type-I spacetimes. Some important conserved quantities for the Lagrangian in this modified theory of gravity are worked out through the determining equations. In this scenario, the graphical behavior of energy density, pressure component and equation of state parameter are reported and analyzed with the help of first integrals of motion. The negative trends of the strong energy conditions actually suggest that the said theory supports expanding Universe with dark energy.

F(mathcal {G}) Noether cosmology

We develop the n-dimensional cosmology for f(mathcal {G}) gravity, where mathcal {G} is the Gauss–Bonnet topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select f(mathcal {G})simeq mathcal {G}^k power-law models where k is a real number. In particular, the case k = 1/2 for n=4 results equivalent to General Relativity showing that we do not need to impose the action R+f(mathcal {G}) to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where f(mathcal {G}) is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.

Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach

The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.

Noether symmetry approach to the non-minimally coupled Y(R)F^2 gravity

We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic properties of these black holes.

Stellar structures in [formula omitted] gravity admitting Noether symmetries

This work aims to investigate some possible emergence of relativistic compact stellar objects in modified f(G) gravity using Noether symmetry approach. For this purpose, we assume static spherically symmetric spacetime in the presence of isotropic matter distribution. We construct Noether symmetry generators along with associated conserved quantities by considering the standard choice of viable f(G) gravity model i.e. f(G)=αGn, where α is the model parameter. In particular, we use conservation relation acquired from the classical Noether approach by imposing some appropriate initial conditions to construct the metric potentials. The obtained conserved quantity play vital role in describing the stellar structure of compact stars. Moreover, by considering an appropriate numerical solution, some salient features of compact stellar structures like effective energy density, pressure, energy conditions, stability against equilibrium of the forces and speed of sound are discussed by assigning the suitable values of model parameter involved. Our study reveals that the compact objects in f(G) gravity from Noether symmetry approach depend on the conserved quantity obtained and the model parameter α. In nutshell, Noether symmetries are quite helpful to generate solutions that follow physically accepted phenomena. Moreover, we observed that these obtained solutions are consistent with the astrophysical observational data, which depicts the viability of our proposed Noether symmetric scheme.