Related papers: Piecewise Conserved Quantities
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
We provide an informal overview of recent developments concerning the singular local limit of nonlocal conservation laws. In particular, we discuss some counterexamples to convergence and we highlight the role of numerical viscosity in the…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These…
The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess a very unphysical property. Specifically, in this model some trajectories are discontinuous functions of their initial…
I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation of Einstein's equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We analyse the boundary structure of General Relativity in the coframe formalism in the case of a lightlike boundary, i.e., when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated…
We focus on the non-linear Schrodinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associated time-like `conserved' quantities and Lax pairs as well as…
We develop a suitable generalization of Almgren's theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic…
The central equations in classical general relativity are the Einstein Field Equations, which accurately describe not only the generation of pseudo-Riemannian curvature by matter and radiation manifesting as gravitational effects, but more…
A spin (dependent) system treatment of gravity is adopted akin to the Sen-Ashtekar treatment. Time is reinserted into the space ``fluid'' at the quantum Level. This time - the Lorentzian one- is shown to be a vorticity of a ``fluid…
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of "conservation laws" has a different meaning. In field theory "conservation laws" are…
Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time…
In this short note, we provide a partial extension of Rivi\`ere's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not…
In this article, several 2+1 dimensional lattice hierarchies proposed by Blaszak and Szum [J. Math. Phys. {\bf 42}, 225(2001)] are further investigated. We first describe their discrete zero curvature representations. Then, by means of…