Coordinate system in general relativity

Uniqueness Theorem for Abstract Hyperbolic Equations with Application to the Uniqueness of the Harmonic Coordinate System in General Relativity

An analog of the radiation condition is found for an abstract hyperbolic equation. When this condition holds, the uniqueness theorem for a&z&u) &(p8,u) + Au = f is valid. Here n, p, and A are some linear operators depending on t and Y. For example, Eq. 0 u = &(uoo(t, X) 8,~) &(u$~u) + q(t, x) u = f is of such a type. In what follows a, = a/a, , ai = a/axi , a, = a/a,. , x = (XI )...) xN), 1 < i...

Prediction in general relativity

Several authors have claimed that prediction is essentially impossible in the general theory of relativity, the case being particularly strong, it is said, when one fully considers the epistemic predicament of the observer. Each of these claims rests on the support of an underdetermination argument and a particular interpretation of the concept of prediction. I argue that these underdeterminati...

The appearance of coordinate shocks in hyperbolic formalisms of General Relativity

I consider the appearance of shocks in hyperbolic formalisms of General Relativity. I study the particular case of the Bona-Massó formalism with zero shift vector and show how shocks associated with two families of characteristic fields can develop. These shocks do not represent discontinuities in the geometry of spacetime, but rather regions where the coordinate system becomes pathological. Fo...

Astrometric tests of General Relativity in the Solar system

Micro-arcsec astronomy is able to verify the predictions of theoretical models of gravitation at a level adequate to constraint relevant parameters and select among different formulations. In particular, this concerns the weak field limit applicable to the Sun neighborhood, where competing models can be expressed in a common framework as the Parametrised Post-Newtonian and Parametrised Post-Pos...

2 Analysis of a Shell System in General Relativity