(ed.). Gravitational waves (IOP, 2001)(422s).

Further reading 401the above that seem to have very good stability properties: [48,51] are among themore recent ones.For the most recent overviews of numerical relativity especially related toblack holes, see the review articles by the author and Wai-Mo Suen: [1, 27, 151–154].18.9.2 Numerical techniquesAn old but still very useful primer on numerical techniques for numericalrelativity can be found in a little article by Smarr in [155]. More moderntreatments for solving PDEs are available in Numerical Recipes [66]. Forhyperbolic systems, the one we learned everything from is [69].18.9.3 Gauge conditionsFor gauge conditions, we recommend the classics: York [10] and Smarr and York[79, 80] for standard maximal slicing and variational principle shift conditions(minimal distortion, etc). For more modern views on how to actually implementsuch conditions more effectively, including the ‘driver’ ideas, see [87] and thevery recent paper [51]. For work on so-called algebraic slicing conditions, see[33, 45], and for problems that can develop with such conditions, see [83, 84].For the most recent ideas on shift conditions, see [156]. There is still a lotof work to do here, especially on shift conditions: please publish some ideasyourselves! This is a crucial area of needed research in numerical relativity thathas not received much attention, especially in 3D.18.9.4 Black hole initial dataThere are by now many black hole initial data sets. There are early references byMisner [157,158], and Brill and Lindquist [115] and then Bowen and York [159],but more recent ones cover the same older material sufficiently. Take a lookat [21,26] and references therein for the classic work. [160] looks at some physicsof initial data sets. For the very large family of distorted black hole plus Brill wavedata sets, check out [161], or including rotation [128]. These were extended to 3Dand discussed briefly in [132]. More recently, important new ways of determininginitial data were developed by Brandt and Bru¨gmann [25]; see also [18, 162].There are many others!18.9.5 Black hole evolution18.9.5.1 Spherical and distorted (axisymmetric) black holesThere have been extensive studies of numerical evolution of distorted black holes.For that we would check out [73] for 1D (spherical, undistorted), [59, 163, 164]for 2D, and finally [128, 129] for 2D rotating black holes.