Related papers: On Gowdy vacuum spacetimes
The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an…
We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a…
In this paper the relations between the asymptotic velocity operators of a quantum system and the asymptotic velocities of the associated Bohmian trajectories are studied. In particular it is proved that, under suitable conditions of…
We prove several global existence theorems for spacetimes with toroidal or hyperbolic symmetry with respect to a geometrically defined time. More specifically, we prove that generically, the maximal Cauchy development of $T^2$-symmetric…
We consider $d>4$-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, the action principle is well-defined \emph{without the need of infinite counter terms.} It naturally…
We analyze the Cauchy problem for symmetric hyperbolic equations with a time singularity of Fuchsian type and establish a global existence theory along with decay estimates for evolutions towards the singular time under a small initial data…
Time-translation symmetry strongly constrains physical dynamics, yet systematic characterization for continuous-variable systems lags behind its discrete-variable counterpart. We close this gap by providing a rigorous classification of…
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…
We investigate the future asymptotic behavior of Gowdy spacetimes on T3, when the metric satisfies weak regularity conditions, so that the metric coefficients (in suitable coordinates) are only in the Sobolev space H1 or have even weaker…
We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for…
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…
Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed,…
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of…
In this contribution we present an overview of our work on the numerical simulation of the perturbation of a black hole space-time by incoming gravitational waves. The formulation we use is based on Friedrich's general conformal equations…
We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states…
This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $\Lambda$. This first paper is concerned with the case of $\Lambda =0$. Our approach is fully based on…
We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in…
The relaxation of a system to a steady state is a central point of interest in many attempts to advance control over the quantum world. In this paper, we consider control through instantaneous Gaussian unitary operations on the ubiquitous…
Wheeler's conjectured "spacetime foam" -- large quantum fluctuations of spacetime at the Planck scale -- could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I…