On the propagation of jump discontinuities in relativistic cosmology

TL;DR

This paper investigates how jump discontinuities propagate in relativistic cosmology, showing the role of constraints in preventing such discontinuities and introducing new hyperbolic evolution systems for specific fluid models.

Contribution

It demonstrates the constraint equations' role in preventing jump discontinuities and introduces new hyperbolic evolution systems for fluid cosmological models.

Findings

Constraints prevent jump discontinuities in derivatives.

Propagation speed of certain modes is 1/2 relative to observers.

New evolution system for G2-invariant fluid models.

Abstract

A recent dynamical formulation at derivative level $\ptl^{3}g$ for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, that employs the concept of evolution systems in first-order symmetric hyperbolic format, implies the existence in the Weyl curvature branch of a set of timelike characteristic 3-surfaces associated with propagation speed $|v| = \sfrac{1}{2}$ relative to fluid-comoving observers. We show it is the physical role of the constraint equations to prevent realisation of jump discontinuities in the derivatives of the related initial data so that Weyl curvature modes propagating along these 3-surfaces cannot be activated. In addition we introduce a new, illustrative first-order symmetric hyperbolic evolution system at derivative level $\ptl^{2}g$ for baryotropic perfect fluid cosmological models that are invariant under the transformations of an Abelian $G_{2}$ isometry group.