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

2021 ◽  
Author(s):  
M. Sharif ◽  
M. Zeeshan Gul
Keyword(s):  
Specific Model ◽  
Compact Objects ◽  
Noether Symmetry ◽  
Model Parameters ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Stellar Objects ◽  
Astrophysical Data ◽  
Symmetry Generators

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.

scholarly journals Compact Stars Admitting Noether Symmetries in Energy-Momentum Squared Gravity

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
M. Sharif ◽  
M. Zeeshan Gul
Keyword(s):  
Initial Conditions ◽  
Early Time ◽  
Coupling Model ◽  
Big Bang ◽  
Compact Objects ◽  
Compact Stars ◽  
Model Parameters ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Stellar Objects

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.

Noether symmetries and anisotropic universe models in f(R, T) gravity

2017 ◽  
Vol 32 (26) ◽  
pp. 1750136 ◽  
Author(s):  
M. Sharif ◽  
Iqra Nawazish
Keyword(s):  
Cosmological Parameters ◽  
Graphical Analysis ◽  
Momentum Tensor ◽  
Anisotropic Universe ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Exponential Expansion ◽  
Symmetry Generators ◽  
Dust Distribution ◽  
Universe Models

This paper investigates the existence of Noether symmetries of some anisotropic homogeneous universe models in non-minimally coupled f(R, T) gravity (R and T represent Ricci scalar and trace of the energy–momentum tensor). We evaluate symmetry generators and the corresponding conserved quantities for two models of this theory admitting direct and indirect non-minimal curvature–matter coupling. We also discuss exact solutions for dust as well as non-dust matter distribution and study the physical behavior of some cosmological parameters through these solutions. For dust distribution, the exact solution corresponds to power-law expansion and Einstein universe while exponential expansion appears for non-dust matter. The graphical analysis of these solutions and cosmological parameters provide consistent results with recent observations about accelerated cosmic expansion. We conclude that Noether symmetry generators and conserved quantities exist for both models.

Conservation laws corresponding to the Noether symmetries of the geodetic Lagrangian in spherically symmetric spacetimes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741006 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze
Keyword(s):  
Conservation Laws ◽  
Noether Symmetry ◽  
Complete List ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given.

Study of Theory about Large Unified Symmetries for Hamilton Systems

2011 ◽  
Vol 27 (2) ◽  
pp. 245-252
Author(s):  
Y.-P. Luo
Keyword(s):  
Lie Symmetry ◽  
Lie Symmetries ◽  
Noether Symmetry ◽  
Theoretical Physics ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Mei Symmetry

ABSTRACTIn this paper, the new concept of theory about Large Unified Symmetries for Hamilton systems are presented. The Large Unified Symmetries and conserved quantities for Hamilton systems are studied by the relation between the three kinds of symmetries and the three kinds of conserved quantities. We worked on the Large Unified Symmetries and conserved quantities by Noether symmetry, Lie symmetry and Mei symmetry, including the definition and criterion of the Large Unified Symmetries and the conserved quantities deduced from them. The Large Unified Symmetries are a intersection set among the Noether symmetries, the Lie symmetries and the Mei symmetries. The theory about Large Unified Symmetries will play an important role in the fields of modern theoretical physics.

A study of Noether symmetries in LRS Bianchi type V spacetimes

2019 ◽  
Vol 35 (06) ◽  
pp. 2050026 ◽  
Author(s):  
Sumaira Saleem Akhtar ◽  
Tahir Hussain
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Bianchi Type ◽  
Noether Symmetry ◽  
Energy Conditions ◽  
Noether Symmetries ◽  
Rotationally Symmetric ◽  
Symmetry Generators ◽  
Type V ◽  
Bianchi Type V

In this paper, we have studied Noether symmetries of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Solving the determining equations of Noether symmetries, it is concluded that the dimension of Noether algebra for these spacetimes is 5, 6, 7, 9, 10, 11 or 17. For all Noether symmetry generators, we have presented the corresponding conservation laws and the Lie algebra. Moreover, some physical implications of the obtained metrics are discussed, which include the study of different energy conditions.

scholarly journals Approximate Mei Symmetries and Invariants of the Hamiltonian

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2910
Author(s):  
Umara Kausar ◽  
Tooba Feroze
Keyword(s):  
Conserved Quantity ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Fields Of Study

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.

scholarly journals $$f(\mathcal {R},\varphi ,\chi )$$ cosmology with Noether symmetry

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
M. Farasat Shamir
Keyword(s):  
Scalar Field ◽  
Modified Gravity ◽  
Vital Role ◽  
Gravity Models ◽  
Noether Symmetry ◽  
Accelerated Expansion ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Cosmic Evolution ◽  
Friedmann Robertson Walker

Abstract This paper is devoted to explore modified $$f(\mathcal {R})$$f(R) theories of gravity using Noether symmetry approach. For this purpose, Friedmann–Robertson–Walker spacetime is chosen to investigate the cosmic evolution. The study is mainly divided into two parts: Firstly Noether symmetries of metric $$f(\mathcal {R})$$f(R) gravity are revisited and some new class of solutions with the help of conserved quantities are reported. It is shown that different scenarios of cosmic evolution can be discussed using Noether symmetries and one of the case indicates the chances for the existence of Big Rip singularity. Secondly, $$f(\mathcal {R})$$f(R) theory coupled with scalar field has been discussed in detail. The Noether equations of modified gravity are reported with three subcases for flat Friedmann–Robertson–Walker universe. It is concluded that conserved quantities are quite helpful to find some important exact solutions in the cosmological contexts. Moreover, the scalar field involved in the modified gravity plays a vital role in the cosmic evolution and an accelerated expansion phase can be observed for some suitable choices of $$f(\mathcal {R},\varphi ,\chi )$$f(R,φ,χ) gravity models.

scholarly journals Classification of Compact Objects: QSS, QSOs, N-Type and Compact Galaxies, Seyfert and Galactic Nuclei

1972 ◽  
Vol 44 ◽  
pp. 97-103
Author(s):  
W. W. Morgan
Keyword(s):  
Galactic Nuclei ◽  
Seyfert Galaxy ◽  
Classification Criteria ◽  
Compact Objects ◽  
Stellar Objects ◽  
Quasi Stellar Objects ◽  
Compact Galaxies

Some methods currently in use for the classification of the optical forms of the ‘compact’ galaxies and quasi-stellar objects are reviewed. It is shown that the category ‘Seyfert Galaxy’ is basically a spectroscopic (rather than a form) classification.An optical form-classification is described which is, in principle, identical with published classification criteria for QSO, N-type, and compact objects. The importance of maintaining rigid form-standards is emphasized.

scholarly journals Determination of exothermic batch reactor specific model parameters

2019 ◽  
Vol 292 ◽  
pp. 01063
Author(s):  
Lubomír Macků
Keyword(s):  
Rate Constant ◽  
Reaction Rate ◽  
Batch Reactor ◽  
Specific Model ◽  
Reaction Rate Constant ◽  
Order Reaction ◽  
First Order Reaction ◽  
Model Parameters ◽  
Reactor Model ◽  
First Order

An alternative method of determining exothermic reactor model parameters which include first order reaction rate constant is described in this paper. The method is based on known in reactor temperature development and is suitable for processes with changing quality of input substances. This method allows us to evaluate the reaction substances composition change and is also capable of the reaction rate constant (parameters of the Arrhenius equation) determination. Method can be used in exothermic batch or semi- batch reactors running processes based on the first order reaction. An example of such process is given here and the problem is shown on its mathematical model with the help of simulations.

scholarly journals Inflationary cosmology in unimodular F(T) gravity

2017 ◽  
Vol 32 (21) ◽  
pp. 1750114 ◽  
Author(s):  
Kazuharu Bamba ◽  
Sergei D. Odintsov ◽  
Emmanuel N. Saridakis
Keyword(s):  
Spectral Index ◽  
Teleparallel Gravity ◽  
Specific Model ◽  
Inflationary Cosmology ◽  
Model Parameters ◽  
De Sitter ◽  
Reconstruction Procedure ◽  
Additional Advantage ◽  
Slow Roll ◽  
Good Agreement

We investigate the inflationary realization in the context of unimodular F(T) gravity, which is based on the F(T) modification of teleparallel gravity, in which one imposes the unimodular condition through the use of Lagrange multipliers. We develop the general reconstruction procedure of the F(T) form that can give rise to a given scale-factor evolution, and then we apply it in the inflationary regime. We extract the Hubble slow-roll parameters that allow us to calculate various inflation-related observables, such as the scalar spectral index and its running, the tensor-to-scalar ratio, and the tensor spectral index. Then, we examine the particular cases of de Sitter and power-law inflation, of Starobinsky inflation, as well as inflation in a specific model of unimodular F(T) gravity. As we show, in all cases the predictions of our scenarios are in a very good agreement with Planck observational data. Finally, inflation in unimodular F(T) gravity has the additional advantage that it always allows for a graceful exit for specific regions of the model parameters.

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