相关论文: Lorentzian dynamics in the Ashtekar gravity
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (``simplicity'' constraints). Within this framework, we underline a…
It is shown - in Ashtekar's canonical framework of General Relativity - that spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time constitutes a finite dimensional completely integrable system. Canonically conjugate…
Empirical understanding teaches us that space is three dimensional while relativity merges space with time. We tried to show that it is possible to model space as three complex coordinates. In our construction, the usual spatial coordinate…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
We investigate a systematic approach to include curvature corrections to the isometry algebra of flat space-time order-by-order in the curvature scale. The Poincar\'e algebra is extended to a free Lie algebra, with generalised boosts and…
We describe the canonical phase space of asymptotically flat gravity in Ashtekar-Barbero variables. We show that the Gauss constraint multiplier must fall off slower than previously considered in order to recover ADM phase space. The…
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
A careful study of the induced transformations on spatial quantities due to 4-dimensional spacetime diffeomorphisms in the canonical formulation of general relativity is undertaken. Use of a general formalism, which indicates the role of…
Some aspects of lightlike dimensional reduction in flat spacetime are studied with emphasis to classical applications. Among them the Galilean transformation of shadows induced by inertial frame changes is studied in detail by proving that,…
Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved…
We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show…
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…
The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to…
In this work, we classify all extended and generalized kinematical Lie algebras that can be obtained by expanding the $\mathfrak{so}\left(2,2\right)$ algebra. We show that the Lie algebra expansion method based on semigroups reproduces not…
We present a novel approach to modified theories of gravity that consists of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show…
We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the…