A class of gauges for the Einstein equations

TL;DR

This paper introduces a new class of gauges for the Einstein vacuum equations within an orthonormal frame formalism, providing hyperbolic systems that ensure local realizability, constraint propagation, and a clear dynamical structure.

Contribution

It presents a novel class of gauges and three symmetric hyperbolic systems for the Einstein vacuum equations, enhancing understanding of their structure and evolution.

Findings

Established gauge conditions for Einstein equations

Derived three symmetric hyperbolic systems

Proved constraint propagation within the formalism

Abstract

A class of gauges for the Einstein vacuum equations is introduced, along with three symmetric hyperbolic systems. The first implies the local realizability of the gauge. The second is the dynamical subset of the field equations. The third is used to show that the constraints propagate. The gauges are for an orthonormal frame formalism, with first order, quadratically nonlinear equations. The unknowns are 16 frame components and 28 connection components. After gauge-fixing, a total of 33 remain.