Related papers: The Noether formalism for constructing conserved q…
We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear…
In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis and spin-connection must be made to obtain a solution from…
We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented in \cite{zhang2020generalized}. Our version of the generalized Noether theorem has several positive features: it is constructed in…
After reminder some facts concerning general relativity ({\bf GR}) we pass to teleparallel gravity. We are confining the special model of the teleparallel gravity, which is popular recently, called {\it the teleparallel equivalent of…
Teleparallel gravity can be seen as a gauge theory for the translation group. As such, its fundamental field is neither the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group. This gauge…
We study the conservation laws in the teleparallel theory with a positive cosmological constant, an extension of the teleparallel theory possessing solutions with de Sitter asymptotics. Demanding that the canonical generators of the…
We derive the affine tensor associated with the energy and momentum densities of both gravitational and matter fields, the complex pseudo-tensor, for $f(Q)$ non-metric gravity, the straightforward extension of Symmetric Teleparallel…
We study the primary constraint structure of Newer General Relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action is built from a scalar formed by quadratic combinations of the nonmetricity…
We examine the teleparallel formulation of non-minimally coupled scalar Einstein-Gauss-Bonnet gravity. In the teleparallel formulation, gravity is described by torsion instead of curvature, causing the usual Gauss-Bonnet invariant expressed…
Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to $|c_{g}/c-1|\gtrsim 10^{-15}$. In this Letter we study the tensorial perturbations in a flat cosmological background…
We exploit an ambiguity somewhat hidden in Noether's theorem to derive systematically, for relativistic field theories, the stress-energy tensor's improvement terms that are associated with additional spacetime symmetries beyond…
We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge-Teitelboim approach. For the embedding theory we consider the coordinate translations on the surface as well as the…
We study a generalized nonlocal theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether Symmetry Approach, we find that the coupling functions coming from…
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity.
In this work, we examine solutions of the system of equations obtained by applying the Noether gauge symmetry (NGS) and its conserved quantity for the standard general relativity (GR) and the non-minimal derivative coupling (NMDC)…
The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models…
In this paper the extension of the functional setting customarily adopted in General Relativity (GR) is considered. For this purpose, an explicit solution of the so-called Einstein's\ Teleparallel problem is sought. This is achieved by a…
We consider the symmetric teleparallel $f\left( Q\right) $-gravity in Friedmann--Lema\^{\i}tre--Robertson--Walker cosmology with nonzero spatial curvature. For a nonlinear $f\left( Q\right) $ model there exist always the limit of General\…
The covariant Noether charge formalism (also known as the covariant phase method) of Wald and collaborators, including its cohomological extension, is a manifestly covariant Hamiltonian formalism that, in principle, allows one to define and…