Related papers: Localized deformation for initial data sets with t…

We give an alternate proof of one of the results given in [16] showing that initial data sets with boundary for the Einstein equations $(M, g, k)$ satisfying the dominant energy condition can be conformally deformed to the strict dominant…

The present work is a natural continuation of the previous paper arXiv:0911.5597. In this work, within the scope of the Generalized Uncertainty Principle, a model of the high energy deformation for a particular case of Einstein's equations…

We apply a new method with explicit solution operators to construct asymptotically flat initial data sets of the vacuum Einstein equation with new localization properties. Applications include an improvement of the decay rate in…

We consider asymptotically Euclidean, initial data sets for Einstein's field equations and solve the localization problem at infinity, also called gluing problem. We achieve optimal gluing and optimal decay, in the sense that we encompass…

In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular…

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of…

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…

Let P be a long range metric perturbation of the Euclidean Laplacian on R^d, d>1. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schroedinger equations associated to P. The problem is decomposed in a low and…

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the…

We prove a localized big bang formation result, which does not require proximity of the initial data to any background solution. Suppose that we are given initial data for the Einstein--nonlinear scalar field equations on an open set $U…

We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…

In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot…

We prove integrated local energy decay for the damped wave equation on stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy decay constitutes a powerful tool in the study of dispersive partial differential…

This work is concerned with the minimization of quantum entropies under local constraints of density, current, and energy. The problem arises in the work of Degond and Ringhofer about the derivation of quantum hydrodynamical models from…

We establish local energy decay for damped magnetic wave equations on stationary, asymptotically flat space-times subject to the geometric control condition. More specifically, we allow for the addition of time-independent magnetic and…

Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is…

We show that models with deformations of special relativity that have an energy-dependent speed of light have non-local effects. The requirement that the arising non-locality is not in conflict with known particle physics allows us to…

We elaborate on the principle that for gapped quantum spin systems with local interaction "local perturbations [in the Hamiltonian] perturb locally [the ground state]". This principle was established in [Bachmann et al. 2012], relying on…

A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…

In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…