Related papers: A New Variable in General Relativity and Its Appli…
This paper explores modifications to General Relativity (GR) by considering higher-order curvature terms in the gravitational action, specifically focusing on the quadratic Ricci scalar and a particular cubic contraction of the Riemann…
We reformulate the general theory of relativity in the language of Riemann-Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed…
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
We identify a symplectic potential for general relativity in tetrad and connection variables that is fully gauge-invariant, using the freedom to add surface terms. When torsion vanishes, it does not lead to surface charges associated with…
The fundamental interactions of nature, the electroweak and the quantum chromodynamics, are described in the Standard Model by the Gauge Theory under internal symmetries that maintain the invariance of the functional action. The fundamental…
We revisit the action principle for general relativity motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise $C^2$ components, each of which can be spacelike, timelike or…
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a…
We study a formulation of euclidean general relativity in which the dynamical variables are given by a sequence of real numbers $\lambda_{n}$, representing the eigenvalues of the Dirac operator on the curved spacetime. These quantities are…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
We introduce a generalized tetrad which plays the role of a potential for torsion and makes torsion dynamic. Starting from the Einstein-Cartan action with torsion, we get two field equations, the Einstein equation and the torsion field…
The tetrad method is used for an introduction of local Lorentz frames and a detailed analysis of local Lorentz transformations. A formulation of equations of motion in local Lorentz frames is based on the Pomeransky-Khriplovich…
In this paper, we investigate the influence of gravity and noncommutativity on Dirac equation. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the…
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
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…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein…
We consider the dynamics of a self-gravitating spinor field and a self-gravitating rotating perfect fluid. It is shown that both these matter distributions can induce a vortex field described by the curl 4-vector of a tetrad: $\omega^i =…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…