Related papers: Energy estimates for the good-bad-ugly model
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact,…
Electromagnetic field produced by magnetic multipoles in hyperbolic motion is derived and compared with electromagnetic field produced by electric multipoles in hyperbolic motion. The resulting fields are related by duality symmetry.…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
We analyse the canonical energy of vacuum linearised gravitational fields on light cones on a de Sitter, Minkowski, and Anti de Sitter backgrounds in Bondi gauge. We derive the associated asymptotic symmetries. When $\Lambda>0$ the energy…
Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical…
Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of…
The hyperboloidal initial value problem is addressed in the context of Numerical Relativity, motivated by its use of hyperboloidal slices - smooth spacelike slices that reach future null infinity, the "place" in spacetime where radiation is…
This thesis is mainly about how to set up and carry out in a physically meaningful way the idea of back-reaction, according to which dark energy could be an effective source. There are, broadly speaking, two distinct approaches. One is…
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…
Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a…
We extend Korevaar-Schoen's theory of metric valued Sobolev maps to cover the case of the source space being an RCD space. In this situation it appears that no version of the `subpartition lemma' holds: to obtain both existence of the limit…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
We develop a general framework for effective equations of expectation values in quantum cosmology and pose for them the quantum Cauchy problem with no-boundary and tunneling wavefunctions. Cosmological configuration space is decomposed into…
We describe a positive energy theorem for Einstein gravity coupled to scalar fields with first-derivative interactions, so-called P(X,phi) theories. We offer two independent derivations of this result. The first method introduces an…
The purpose of this paper is to show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small…
We consider the focussing energy-critical inhomogeneous nonlinear Schr\"odinger equation: $$ iu_t + \Delta u + g|u|^2u = 0, u(0)= \varphi \in \dot{H}^1,\;\; 0 \le g_i \le |x|g \le g_s.$$ On the road map of Kenig-Merle \cite{km} we show the…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field…
Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which…