Related papers: Einstein Gravity, Lagrange-Finsler Geometry, and N…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
We develop a semiclassical theory of modified gravity with nontrivial spacetime torsion. In particular, we show that the semiclassical treatment can be axiomatized in the case of Einstein--Cartan theory with a nonminimally coupled, free…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
We relate the Teichmuller spaces obtained by Hitchin to the Teichmuller spaces of $WA_{n}$-gravity. The relationship of this space to $W$-gravity is obtained by identifying the flat $PSL(n+1,{\BR})$ connections of Hitchin to generalised…
The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a…
We construct a metric-like formulation of the non-relativistic (NR) limit of bosonic supergravity at the Lagrangian level. This formulation is particularly useful for decomposing relativistic tensors, such as powers of the Riemann tensor,…
The notions of the interior and truncated connections of a nonholonomic manifold are introduced. A class of extended truncated connections is distinguished. For the case of a contact space with a Finsler metric, it is shown that there…
In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not ``fundamental'' but rather is an almost automatic low-energy long-distance consequence of a wide class of theories.…
The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a…
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the…
Finslerian extensions of Special and General Relativity -- commonly referred to as Very Special and Very General Relativity -- necessitate the development of a unified Lorentz-Finsler geometry. However, the scope of this geometric framework…
Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent…
Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq 2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$ defining…