相关论文: Noether symmetry in the higher order gravity theor…
We explore Noether symmetries of Horndeski gravity, extending the classification of general scalar-tensor theories. Starting from the minimally coupled scalar field and the first-generation scalar-tensor gravity, the discussion is…
In this paper, we investigate the newly developed $f(R,\mathbf{T}^2)$ theory ($R$ is the Ricci scalar and $\mathbf{T}^2=T_{\alpha\beta}T^{\alpha\beta},~T _{\alpha\beta}$ demonstrates the energy-momentum tensor) to explore some viable…
Unlike Noether symmetry, a metric independent general conserved current exits for non-minimally coupled scalar-tensor theory of gravity, if the trace of the energy momentum tensor vanishes. Thus, in the context of cosmology, a symmetry…
Since the general theory of relativity (GR) meets some difficulties, it seems that new considerations on the ether theories of gravitation in the history are needed. A theory of gravity based on some new concepts of ether and particles is…
This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…
The article is devoted to the investigation of the Noether currents and integrals of motion in the special subclass of theories with higher field derivatives -- theories under differential field transformations in action (DFTA). Under…
This paper is devoted to investigate the recently proposed modified Gauss-Bonnet $f(\mathcal{G},T)$ gravity, with $\mathcal{G}$, the Gauss-Bonnet term, coupled with ${T}$, the trace of energy-momentum tensor. We have used the Noether…
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…
A class of autonomous, even-order ordinary differential equations is discussed from the point of view of Lie symmetries. It is shown that for a certain power nonlinearity, the Noether symmetry group coincides with the Lie point symmetry…
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is…
The Noether procedure carries an inherent ambiguity due to the necessary local extension, no longer a symmetry, of the global symmetry. The gauging should fix the ambiguity once and for all, however, and, for translations, the general…
The Noether symmetry issue for Horndeski Lagrangian has been studied. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have…
We investigate the main features of the flat Friedmann-Lema{\i}tre-Robertson-Walker cosmological models in the f(T) teleparallel gravity. In particular, a general approach to find out exact cosmological solutions in f (T) gravity is…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the "cosmic…
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…
Unlike F(R) gravity, pure metric F(T) gravity in the vacuum dominated era, ends up with an imaginary action and is therefore not feasible. This eerie situation may only be circumvented by associating a scalar field, which can also drive…
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating…
New symmetry theorems are obtained for field theories formulated in Minkowski spacetime, based on the recognition that such theories should be diffeomorphism invariant. These theorems, which are in fact generalized Noether theorems, have…
Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions.…