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

402 Numerical relativity18.9.5.2 Colliding black holesFor colliding Misner black holes, the original work of Smarr and others isremarkable: see [165–167]. For a more advanced attempt see [168, 169]. Forboosted black holes, see [170], and for unequal mass black hole collisions see[171]. For an alternative type of black hole collision, with particles forming blackholes, see [110] and references therein.18.9.5.3 3D black holesIn 3D, so far little has been published. 3D Schwarzschild was evolved numericallyby [45, 60]. Distorted 3D black holes were studied numerically, and compared toperturbation theory for the first time, in [131, 132].Colliding black holes in 3D were studied in [172], and the first full 3Dcollisions were performed in [2, 147].For a completely alternative approach to that considered here, characteristicevolution techniques have been used very successfully to evolve black holes in [8].18.9.6 Black hole excisionFor black hole excision, see [105] for an early 1D success (but the idea wasfloating around long before). Then [173] followed up with a more advancedtreatment. Other successful 1D work includes [43, 109, 174]. [6, 7, 45, 60] givethe first successful, and increasingly complex, 3D attempts.18.9.7 Perturbation theory and waveform extractionFor work on the perturbative/numerical synergy approach, there are many papers.The original that really started it all, for Misner data, was [175], followed by[176], and with boosted holes, [170]. An extraordinary paper that carries theMisner problem to second order is [177]. [178] gives a review. For the movetowards the Teukolsky formalism for rotating black holes, see [179–181], amongothers.For the first attempts to use perturbation theory for 3D distorted black holes,showing the incredible accuracy one can achieve in waveforms, see [132].18.9.8 Event and apparent horizonsFor a nice description of the apparent and event horizons, see [182]. Techniquesto find apparent horizons abound; the most recent variations can be found in[124, 125, 145, 183, 184].Two different event horizon finding methods are described in [103,110]; thelatter method is used now by all groups we are aware of. More details of themethod can be found in [104].