Related papers: Asymptotically constrained and real-valued system …
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of…
The relation between the Husain-Kucha\v{r} model and some extensions thereof that incorporate a dynamical time variable is explored. To this end, we rely on the geometric approach to the Hamiltonian dynamics of singular (constrained)…
In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short…
We introduce a reduced model for a real sector of complexified Ashtekar gravity that does not correspond to a subset of Einstein's gravity but for which the programme of canonical quantization can be carried out completely, both, via the…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
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…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We,…
A Hilbert manifold structure is described for the ADM phase space of asymptotically flat initial data $(g,\pi)$ with local $H^2\times H^1$ Sobolev regularity. Solutions of the constraint equations form a Hilbert submanifold. A regularized…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
In a previous paper we formulated axisymmetric general relativity in terms of real Ashtekar--Barbero variables. Here we proceed to quantize the theory. We are able to implement Thiemann's version of the Hamiltonian constraint. We discuss…
The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…
We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the…
It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…
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 study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak…
In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the…