Related papers: Generalized forms, metrics and Ricci flat four-met…
We study the field equations of modified theories of gravity in which the lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the…
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We show that the space of solutions of a wide family of Ricci-based metric-affine theories of gravity can be put into correspondence with the space of solutions of general relativity (GR). This allows us to use well-established methods and…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
We show that Einstein's main equations for stationary axisymmetric fields in vacuum are equivalent to the motion equations for bosonic strings moving on a special nonflat background. This new representation is based on the analysis of…
Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$…
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…
We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in QFT force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
Lorentzian 4-metrics are expressed in spinorial coordinates. In these coordinates the metric components can be factorized into a product of complex conjugate quantities. The linearized theory and Einstein's vacuum field equations are…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…