I’ve just finished Jörg Frauendiener’s, “On the applicability of constrained symplectic integrators in general relativity”. It’s a readable paper (the necessary background is given in the paper) about numerical integration in Hamiltonian systems. The idea here is that if we have a symplectic manifold modelling the states of some system of ODE’s, along with a …
Category Archive: Papers
Is general relativity “essential understood”?
Predictably the papers answer is no. Why? Because current numerical methods in general relativity are limited. The paper implies that these limitations are Inability to compute global solutions Inability to evolve initial data for strongly gravitating and very dynamic systems. In any case Friedrich then divides the field equations to four classes the system of …
Derived smooth manifolds
Despite not working in algebra I’m a sucker for it. So when I came across an article on derived smooth manifolds I knew I had to have a look. The phrase “derived X”, when used in a mathematical context usually refers to some category of objects which is built out of a category describing the …
Nature of singularities in gravitational collapse
A very terse article giving an overview of the state of cosmic censorship in 99/00. Given it’s brevity I recommend a technical background in the differential topological techniques of GR. I assume that the article was written specifically for the conference proceedings, as this would explain a lot. Despite the lack of exposition I still …
Properties of global time functions
I’ve been spending a lot of time rereading a number of older papers on stable causality. Basically I want to get a handle on the types of techniques needed to manipulate them. For this Seifert’s 1977 paper is a gem. My particular interest is on the extension of a time function from a compact neighbourhood …