Related papers: Solution of the noncanonicity puzzle in General Re…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…
We argue that there is nothing puzzling in the fact that the Hamiltonian formulation of a covariant theory, General Relativity, after a non-covariant change of field variables is not canonically related to the formulation based on the…
It is shown that the Hamiltonian of the Einstein affine-metric (first order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the…
A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…
We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the $3+1$-decomposition of spacetime, we…
In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the…
Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent…
Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position,…
Our attempts to find an explanation for quantum behavior of the Early Universe appeal, as a rule, to the Wheeler - DeWitt Quantum Geometrodynamics which relies upon Hamiltonian formulation of General Relativity proposed by Arnowitt, Deser…
We apply the ADM approach to obtain a Hamiltonian description of the Einstein-Hilbert action. In doing so we add four new ingredients: (i) We eliminate the diffeomorphism constraints. (ii) We replace the densities $\sqrt g$ by a function…
The authors present concepts and mathematical developments which give rise to the Hamiltonian formulation of Einstein's general relativity, first introduced by Arnowitt, Deser, and Misner. All the geometrical quantities needed for the…
In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [1]. The implementation is made with the aid of a symmetric stress-energy tensor and not a…
Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…
About 50 years ago, in 1958, Dirac published his formulation of generalized Hamiltonian dynamics for gravitation. Several years later Arnowitt, Deser and Misner (ADM) proposed their description of the dynamics of General Relativity which…
Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a…
The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pre-geometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with…
We generalize the 1+1-dimensional gravity formalism of Ohta and Mann to 3+1 dimensions by developing the canonical reduction of a proposed formalism applied to a system coupled with a set of point particles. This is done via the…
We obtain the Arnowitt-Deser-Misner formulation of general relativity in $n$ dimensions ($n \geq 3$) from its either $SO(n-1,1)$ [$SO(n)$] or $SO(n-1)$ Palatini Hamiltonian formulations and vice versa [we recall that $SO(n-1,1)$ [$SO(n)$]…
This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…