Distributional geometry in general relativity

Nonlinear distributional geometry and general relativity

This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau’s special setting) and its applications to general relativity with a special focus on the distributional description of impulsive gravitational waves.

From Spinor Geometry to Complex General Relativity

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component spinor calculus, conformal gravity, α-planes in Minkowski space-time, α-surfaces and twistor geometry, anti-self-dual space-times and Penrose transform, spin-3/2 potentials, heave...

Semi-Riemann Geometry and General Relativity

General very special relativity is Finsler geometry

G. W. Gibbons, Joaquim Gomis, and C. N. Pope DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, United Kingdom Departament ECM, Facultat de Fı́sica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A&M University, College Station, Texas 77843-4242, USA (Rece...

On Hypermomentum in General Relativity III. Coupling Hypermomentum to Geometry

I n Par t 1 1 of th is series we presented the not ion of the mate r ia l hypermomentum cur ren t and mot ivated i ts i n t r o d u c t i o n in to genera l re la t i v i t y . I n Par t I I 2 we showed tha t a general, l i near l y connected m a n i f o l d w i t h symmet r i c me t r i c ( L 4 , g) is the appropr ia te geometr ica l f ramework fo r such an i n t roduc t i on . T h e present p...