General relativity and Weyl geometry

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.

Semi-Riemann Geometry and General Relativity

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...

Eigenvalues of the Weyl Operator as Observables of General Relativity

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as gravitational variables, and derive explicit formulas for their Poisson brackets and their time evolution. P.A.C.S. number:+04.20,04.90 On leave from Dipartimento di Fi...

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...