相关论文: Lorentzian dynamics in the Ashtekar gravity
One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to…
In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the solutions of the so-called simplicity…
We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge…
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $\Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the 2-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions…
We consider special classes of Palatini f(R) theories, featured by additional Loop Quantum Gravity inspired terms, with the aim of identifying a set of modified Ashtekar canonical variables, which still preserve the SU(2) gauge structure of…
We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central…
In this article we give a full description of the dynamics of the flat anisotropic (4+1)-dimensional cosmological model in the presence of both Gauss-Bonnet and Einstein contributions. This is the first complete description of this model…
Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar formulation, when the spatial manifold is a torus. We have found a set of globally defined observables, forming a closed algebra. This allowed us to solve the quantum…
We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two $SO(3)$ connections. We analyze first the Husain-Kucha\v{r} model and find a two connection description for it. Introducing a…
A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve…
The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized…
Beginning from the Ashtekar formulation of canonical general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by gauge-fixing the gravitational fields within a complex of…
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…
Related to the classical Ashtekar Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1)- and (3+1)-dimensions, and also generalizations of Einstein's theory of gravity. In this review, I will try to…
As shown by Ashtekar in the mid 80's, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an {\it alternative}…
In this paper, we prove Lorentzian positive mass theorem for spacetimes with distributional curvature. To do so, we introduce distributional curvature and generalized Arnowitt-Deser-Misner (ADM) momentum. As an application, we discuss a…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are…