Displaying similar documents to “Hyperbolic methods for Einstein's equations.”

Well posed reduced systems for the Einstein equations

Yvonne Choquet-Bruhat, James York (1997)

Banach Center Publications


We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.

Blow-up for solutions of hyperbolic PDE and spacetime singularities

Alan D. Rendall (2000)

Journées équations aux dérivées partielles


An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful...

The hyperbolic triangle centroid

Abraham A. Ungar (2004)

Commentationes Mathematicae Universitatis Carolinae


Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive objects with equal masses located at the triangle vertices. Employing gyrovector space techniques...