Symmetries of spacetime and their relation to initial value problems

TL;DR

This paper demonstrates that in certain covariant gravity-matter systems, the evolution preserves initial symmetries, linking spacetime symmetries to initial value problem properties in hyperbolic PDE frameworks.

Contribution

It establishes that symmetry properties of initial data are maintained during evolution in a class of covariant gravity-matter theories with hyperbolic reductions.

Findings

Symmetry preservation during evolution in gravity-matter systems

Conditions for hyperbolic reduction of matter equations

Relationship between initial data symmetries and spacetime evolution

Abstract

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential equations can be deduced from the matter field equations. Second, gravity is supposed to be coupled to the matter fields by requiring that the Ricci tensor is a smooth function of the basic matter field variables and the metric. It is shown then that the ``time'' evolution of these type of gravity-matter systems preserves the symmetries of initial data specifications.