Related papers: The Biconnection Variational Principle for General…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
The criterion of differentiability of functions of quaternion variable is used as the basis of some algebraic field theory. Its necessary consequences are free Maxwell and Yang-Mills equations. The differentiability equations may be…
The use of the bivectors in the General Relativity with Newman-Penrose formalism is important to the description of the exact solutions of the Einstein's field equations. This review is devoted to introduce the basic ideas with calculation…
Current generalizations of the classical Einstein-Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles are known to reproduce Einstein's gravitational equations, and should therefore be…
We consider a specific Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, where the canonical variables are expressed by means of differential forms. We show that some ``position'' variables of this formulation…
A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in…
A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…
The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of ``observables'' for general relativity. Recent work of Chamseddine and Connes suggests that…
We study the frame dependence/independence of cosmological observables under disformal transformations, extending the previous results regarding conformal transformations, and provide the correspondence between Jordan-frame and…
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
We argue that in the general relativistic calculation of planetary orbits, the choice of a reference frame which is an obligatory condition in the Newtonian approach is replaced by an appropriate boundary condition on the solution of…
As basic variables in general relativity (GR) are chosen antisymmetric connection and bivectors - bilinear in tetrad area tensors subject to appropriate (bilinear) constraints. In canonical formalism we get theory with polinomial…
We postulate the applicability of the general form-invariance principle in special relativity. It is shown that this principle holds in classical mechanics. Some examples of transformations between the reference frames which satisfy this…
We study general metric-affine theories of gravity in which the metric and connection are the two independent fundamental variables. In this framework, we use Lagrange-Noether methods to derive the identities and the conservation laws that…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
Following a conjecture of Feynman, we explore the possibility that only those energy forms that are associated with (massive or massless) particles couple to the gravitational field, but not others. We propose an experiment to deflect…