Related papers: Note on conserved currents in static Conformal Kil…
The collapsing dynamics of relativistic fluid are explored in $f(R)$ gravity in a detailed systematic manner for the non-static spherically symmetric spacetime satisfying the equation of the conformal Killing vector. With quasi-homologous…
We study the Teleparallel Equivalent of General Relativity (TEGR) with Lagrangian that includes the flat (inertial) spin connection and that is evidently invariant with respect to local Lorentz rotations. Applying directly the Noether…
We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to…
New Lagrangians, depending on the field strengths and the electric and magnetic sources are found, which lead to the Maxwell equations. One new feature is that the equations of motion are obtained by varying the Lagrangian with respect to…
Gauge invariant conserved conformal currents built from massless fields of all spins in 4d Minkowski space-time and $AdS_4$ are described within the unfolded dynamics approach. The current cohomology associated with non-zero conserved…
We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of St\"ackel-Killing and Killing-Yano tensors is pointed out. Some nontrivial…
In this paper we discuss the construction of conserved tensors (currents) involving conformal Killing-Yano tensors (CKYTs), generalising the corresponding constructions for Killing-Yano tensors (KYTs). As a useful preparation for this, but…
Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the…
In this article, I discuss the construction of some globally conserved currents that one can construct in the absence of a Killing vector. One is based on the Komar current, which is constructed from an arbitrary vector field and has an…
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…
The study of long wavelength scalar perturbations, in particular the existence of conserved quantities when the perturbations are adiabatic, plays an important role in e.g. inflationary cosmology. In this paper we present some new conserved…
We give a new construction of conserved charges in asymptotically anti-de Sitter spacetimes in Einstein's gravity. The new formula is explicitly gauge-invariant and makes direct use of the linearized curvature tensor instead of the metric…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
Very recently Harada has proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is…
Covariant conserved 2-form currents for linearised gravity are constructed by contracting the linearised curvature with conformal Killing-Yano tensors. The corresponding conserved charges were originally introduced by Penrose and have…
We consider $f\left(R\right) $-gravity in a Friedmann-Lema\^itre-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right) $ and…
A general scalar-tensor theory of gravity carries a conserved current for a trace free minimally coupled scalar field, under the condition that the potential $V(\phi)$ of the nonminimally coupled scalar field is proportional to the square…
We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to…
We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the…