Related papers: A covariant Hamiltonian tetrad approach to numeric…
We present Hamilton's equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the…
The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames…
In a recent work we derived the kinematic Hamiltonian and primary constraints of the new general relativity class of teleparallel gravity theories and showed that these theories can be grouped in 9 classes, based on the presence or absence…
A systematic Hamiltonian formulation of the Einstein-Cartan system, based on the Hilbert-Palatini action with the Barbero-Immirzi and cosmological constants, is performed using the traditional ADM decomposition and without fixing the time…
The canonical formalism of the (2+2) formulation of general relativity of 4 spacetime dimensions is studied under no symmetry assumptions, where the spacetime is viewed as a local product of a 2 dimensional base manifold of Lorentzian…
General relativity contains 16 variables in the framework of ADM-Vielbein formalism which are 6 more than metric formalism. These variables emerge due to additional symmetry of Local Lorentz Transformations. In the framework of the…
A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength…
We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
It is known that one can formulate an action in teleparallel gravity which is equivalent to general relativity, up to a boundary term. In this geometry we have vanishing curvature, and non-vanishing torsion. The action is constructed by…
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…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of…
In the context of the teleparallel equivalent of general relativity we establish the Hamiltonian formulation of the unimodular theory of gravity. Here we do not carry out the usual $3+1$ decomposition of the field quantities in terms of the…
The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the…
After a study of the Hamiltonian group of gauge transformations of canonical tetrad gravity on globally hyperbolic, asymptotically flat at spatial infinity, spacetimes with Cauchy hypersurfaces $\Sigma_{\tau}$ diffeomorphic to $R^3, we find…
The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically…
Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is…
Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian space-time, tetrads, connection one-forms,…
The basic and fundamental aspects of General Relativity are in general analysed in mathematical level of coordinate basis or holonomic frame by several authors in the literature. However, for many purposes it is more convenient to use a…