Related papers: General structure of the solutions of the Hamilton…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
We study a generalized Einstein theory with the following two criteria:{\it i}) on the solar scale, it must be consistent with the classical tests of general relativity, {\it ii}) on the galactic scale, the gravitational potential is a sum…
By applying the method of moving frames modelling one and two dimensional local anisotropies we construct new solutions of Einstein equations on pseudo-Riemannian spacetimes. The first class of solutions describes non-trivial deformations…
We perform the Hamiltonian analysis of general bimetric gravity. We determine four first class constraints that are generators of the diagonal diffeomorphism. We further analyze the remaining constraints and we present an evidence that…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
We consider the dilaton gravity models derived by reductions of generalized theories of gravity and study one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully…
We complete the program started in two companion papers of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The case of General Relativity is addressed by…
We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric…
It is argued that the solution space of the equation determining the class of $f(R)$ theories which admit an Einstein static universe should be broadened by including the algebraic roots.
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
In current paper we refer to the geometrical classification of the Einstein equations which has been developed by one of the authors of this paper. This classification was based on the classical theory for decomposition of the tensor…
In this paper we shall address this problem: Is quantum gravity constraints algebra closed and what are the quantum Einstein equations. We shall investigate this problem in the de-Broglie--Bohm quantum theory framework. It is shown that the…
We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain…
We study two-dimensional F(R) Horava-Lifshitz gravity from the Hamiltonian point of view. We determine constraints structure with emphasis on the careful separation of the second class constraints and global first class constraints. We…
We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.
The stability of the Einstein static universe against the homogeneous scalar perturbations in $f(T)$ gravity is analyzed. Both the spatial closed and open universes are considered. We find that the stable Einstein static solutions exist in…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…