### 4.4 Other hyperbolic formulations

There exist many other hyperbolic reductions of Einstein’s field equations. In particular,
there has been a large amount of work on casting the evolution equations into first-order
symmetric [2, 182, 195, 3, 21, 155, 248, 443, 22, 74, 234, 254, 383, 377, 18, 285, 285, 86] and
strongly hyperbolic [62, 63, 12, 59, 60, 13, 64, 367, 222, 78, 58, 82] form; see [182, 352, 188, 353] for
reviews. For systems involving wave equations for the extrinsic curvature; see [128, 2]; see also [424]
and [20, 75, 374, 379, 436] for applications to perturbation theory and the linear stability of solitons and
hairy black holes.
Recently, there has also been work deriving strongly or symmetric hyperbolic formulations from an
action principle [79, 58, 243].