Invariant Algebraic Slicing of the Spacetime

TL;DR

This paper develops a fully first order formulation of the evolution system in general relativity using invariant algebraic slicing, explicitly characterizing the characteristic fields and relating gauge speeds to light speed.

Contribution

It introduces a class of invariant algebraic slicing conditions and explicitly derives the characteristic fields and speeds, enhancing understanding of gauge dynamics in spacetime evolution.

Findings

Characteristic speeds related to gauge are equal to light speed

Explicit set of characteristic fields provided

First order invariant algebraic slicing conditions formulated

Abstract

Using the momentum constraint, the standard evolution system is written in a fully first order form. The class of first order invariant algebraic slicing conditions is considered. The full set of characteristic fields is explicitly given. Characteristic speeds associated to the gauge dependent eigenfields (gauge speeds) are related to light speed.