Related papers: New considerations on Hilbert action and Einstein …
We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for quantum fluctuation of the inflation…
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…
Standard general relativity fails to take into account the changes in coordinates induced by the variation of metric in the Hilbert action principle. We propose to include such changes by introducing a fundamental compensating tensor field…
Upon straightforward four--directional extension of the special--relativistic two--dimensional transformations to the four--dimensional case we lead to convenient totally anisotropic kinematic transformations, which prove to reveal many…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
We report on recent developments towards a relativistic quantum mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and…
We show that the conservation laws for the geodesic equation which are associated to affine symmetries can be obtained from symmetries of the Lagrangian for affinely parametrized geodesics according to Noether's theorem, in contrast to…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar…
We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being…
The paper extends basic Einstein--Hilbert action by adding a newly proposed invariant constructed from a specific contraction between the Einstein tensor and the energy momentum tensor, encoding a non--minimal coupling between the…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We revisit the physical arguments which lead to the definition of the stress-energy tensor $T$ in the Lorentz-Finsler setting $(M,L)$ starting at classical Relativity. Both the standard heuristic approach using fluids and the Lagrangian one…
In Einstein-Cartan theory, by the use of the general Noether theorem, the general covariant angular-momentum conservation law is obtained with the respect to the local Lorentz transformations. The corresponding conservative Noether current…
We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian coordinates. We compute variational symmetries of the action functional and generate…
We consider the Einstein equation, where the common electromagnetic energy momentum tensor is replaced by its generalized equivalent as suggested in our earlier paper (A.L. Kholmetskii et al. Phys. Scr. 83, 055406 (2011)). Now we show that…
We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for physics; they guarantee well defined…