Related papers: On dRGT massive gravity with degenerate reference …
In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H\"{o}lder's inequalities…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially…
It is commonly believed that the dRGT theory is the unique way to describe a massive spin-2 field without ghosts. While dRGT is arguably the most elegant massive gravity theory, it seems that it may not be the unique ghost-free one if one…
We construct a conserved, symmetric energy-momentum (pseudo-)tensor for Chern-Simons modified gravity, thus demonstrating that the theory is Lorentz invariant. The tensor is discussed in relation to other gravitational energy-momentum…
In certain modified theories of gravity, non-minimal couplings between matter and geometry lead to the nonconservation of the energy-momentum tensor. By interpreting this as an effective dissipative process, we formulate a general class of…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
We present two different versions of the consistent theory of massive gravitons in arbitrary spacetimes which are simple enough for practical applications. The theory is described by a non-symmetric rank-2 tensor whose equations of motion…
Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential can be discussed in a unitary way, both in the Lagrangian and canonical frameworks, by introducing suitable field redefinitions. The new fields are directly…
In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries…
We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under…
The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…
We consider the standard gauge theory of Poincar\'{e} group, realizing as a subgroup of $GL(5. R)$. The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this…
The notions of (metric) hypersurface data were introduced in [Mars,2013] as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-riemannian manifolds. In this paper, general geometric properties of…
We consider the lagrangian $L=F(R)$ in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein's theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians…
We study algebraic type N spacetimes in the extended new massive gravity (NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG with any finite order curvature corrections. We show that for these spacetimes, the field…
Matter collineations of locally rotationally symmetric spacetimes are considered. These are investigated when the energy-momentum tensor is degenerate. We know that the degenerate case provides infinite dimensional matter collineations in…
We perform a systematic study of various versions of massive gravity with and without violation of Lorentz symmetry in arbitrary dimension. These theories are well known to possess very unusual properties, unfamiliar from studies of gauge…
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the…