Related papers: Evolutionary constraints: Gluing in a toy model
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
In this paper we are concerned with the number of critical points of solutions of nonlinear elliptic equations. We will deal with the case of non-convex, contractile and non-contractile planar domains. We will prove results on the estimate…
Two new methods have been proposed for solving the gravitational constraints without using elliptic solvers by formulating them as either an algebraic-hyperbolic or parabolic-hyperbolic system. Here, we compare these two methods and present…
It is shown that, by an appropriate modification of the structure of the interaction potential, the Breit equation can be incorporated into a set of two compatible manifestly covariant wave equations, derived from the general rules of…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…
In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
Many astrophysical problems, ranging from structure formation in cosmology to dynamics of elliptical galaxies, refer to slow processes of evolution of essentially collisionless self-gravitating systems. In order to determine the relevant…
This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler…
Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as…
We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for…
In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…
The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a…