Related papers: Abelian Ashtekar formulation from the ADM action
We consider $\Lambda$=0 three dimensional gravity with asymptotically flat boundary conditions. This system was studied by Ashtekar and Varadarajan within the second order formalism -with metric variables- who showed that the…
We discuss linearized gravity from the point of view of a gauge theory. In (3+1)-dimensions our analysis allows to consider linearized gravity in the context of the MacDowell-Mansouri formalism. Our observations may be of particular…
Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
This article studies a numerical relativity approach to the initial value problem in Anti-de Sitter spacetime relevant for dual non-equilibrium evolution of strongly coupled non-Abelian plasma undergoing Bjorken expansion. In order to use…
We argue that the conclusion, `we cannot consider the Dirac approach as fundamental and undoubted', made in the paper by Shestakova (Class. Quantum Grav. 28 055009, 2011), is based upon an incomplete and flawed analysis of the simple model…
Solutions are constructed to the quantum constraints for planar gravity (fields dependent on z and t only) in the Ashtekar complex connection formalism. A number of operators are constructed and applied to the solutions. These include the…
The constraint hypersurfaces defining the Witten and Ashtekar formulations for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of several sectors that intersect…
This paper delves into the exploration of suitable boundary conditions for the asymptotically flat scenario of general relativity presented in terms of Ashtekar-Barbero variables. While the standard parity conditions have been extensively…
By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation…
We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy…
Starting from a Hamiltonian description of four dimensional general relativity in presence of a cosmological constant we perform the program of canonical quantisation. This is done using complex Ashtekar variables while keeping the…
A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to $R^3$ is obtained by using a new parametrization of arbitrary cotetrads to define a set of…
The Hamiltonian formulation of the gravitational sector of the Standard-Model Extension (SME) with nondynamical fields $u$ and $s^{\mu \nu}$ is studied. We provide the relevant Hamiltonians that describe the constrained phase space and the…
Barbero recently suggested a modification of Ashtekar's choice of canonical variables for general relativity. Although leading to a more complicated Hamiltonian constraint this modified version, in which the configuration variable still is…
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…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…
In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar…