Nonlinear wave equations for relativity

Gravitational wave motion is described by nonlinear wave equations using the tetrad and its connection as field variables. The wave equations result from a Lorentz gauge on the connections. This description separates the physics of wave motion from the causal structure, which is evolved in the tangent space. The initial data constraints are derived in this approach using Yang-Mills scalar and vector potentials, resulting in Lie constraints associated with the additional Poincaré gauge invariance. The analogy of the constraint equations with those in Ashtekar's variables is emphasized.