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 [2Jump To The Next Citation Point, 182Jump To The Next Citation Point, 195, 3, 21, 155, 248, 443, 22Jump To The Next Citation Point, 74, 234, 254Jump To The Next Citation Point, 383, 377, 18, 285Jump To The Next Citation Point, 285, 86] and strongly hyperbolic [62, 63, 12, 59, 60, 13, 64, 367, 222, 78, 58Jump To The Next Citation Point, 82Jump To The Next Citation Point] form; see [182Jump To The Next Citation Point, 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].


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