Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing

TL;DR

This paper reformulates Einstein and Yang-Mills theories in a gauge-invariant, hyperbolic form that is suitable for analysis and numerical computation, avoiding gauge-fixing.

Contribution

It introduces a gauge-invariant hyperbolic formulation of Einstein and Yang-Mills equations, facilitating analysis and simulations without gauge-fixing.

Findings

Equations can be written in flux-conservative symmetric hyperbolic form

Formulation is suitable for global analysis and numerical methods

Avoids gauge-fixing in the dynamical equations

Abstract

The evolution of physical and gauge degrees of freedom in the Einstein and Yang-Mills theories are separated in a gauge-invariant manner. We show that the equations of motion of these theories can always be written in flux-conservative first-order symmetric hyperbolic form. This dynamical form is ideal for global analysis, analytic approximation methods such as gauge-invariant perturbation theory, and numerical solution.