Numerical Simulations of Black Holes  

In General > s.a. black holes; horizons / initial-value formulation.
* Approach: Traditionally, use finite difference methods, often plagued by instabilities; The three stages of binary black hole evolution require different techniques (pre-merger uses PN formalism up to O(v7), merger is numerical, post-merger–ringdown uses quasinormal modes).
* 2003: Stable gauge, M Alcubierre.
* 2004: Stable "long-term" evolution with first full binary orbit, B Brügmann at AEI.
* 2005: First full orbit and merger, achieved by various groups with technique by F Pretorius that uses punctures rather than excisions.
* 2006: M Campanelli et al, J Baker et al, moving punctures to handle singularities.
* 2010: High-accuracy simulations of inspiral and merger events are done, but still take way too much time to be able to run many.
@ References: Sperhake et al a1107/CRAS [rev].

Single Black Holes > s.a. black-hole solutions.
@ General references: Brügmann PRD(96)gq [adaptive mesh]; Gómez et al (BBHGCA) PRL(98)gq; Hübner CQG(99) [boundaries]; Scheel et al PRD(02); Brandt et al CQG(03)gq/02 [data]; Anderson & Matzner FP(05)gq/03 [long term evolution]; Bishop et al PRD(03) [Schwarzschild + massive particle]; Tichy PRD(09)-a0911 [long-term evolution, pseudospectral methods]; Yo et al PRD(12)-a1205 [modified BSSN formulation, numerical stability].
@ From particle collisions: Choptuik & Pretorius PRL(10)-a0908 [ultra-relativistic], news sci(10)jan.
@ Spherically symmetric: Bona et al PRD(95)gq/94; Thornburg gq/99/PRD; Brewin gq/00-MG9; Ruíz et al GRG(08)-a0706 [and axisymmetric, regularization]; Brewin PRD(12)-a1101 [Schwarzschild spacetime, Einstein-Bianchi system].
@ Axisymmetric: Brandt & Font gq/97-MG8; Gleiser al et PRD(98)gq/97 [spinning black hole]; Garfinkle & Duncan PRD(01)gq/00 [Brill waves]; Rinne PhD(05)gq/06; Vasset et al a1002-MG12 [excised Kerr spacetime].
@ Perturbations: Krivan et al PRD(97) [Kerr, effects]; Brandt et al gq/97-MG8; Papadopoulos et al PRD(98)gq [gravitational waves]; Loustó CQG(05)gq [fourth-order algorithm, extreme-mass-ratio Zerilli & Regge-Wheeler]; > s.a. black-hole perturbations.
@ Other black holes: Karkowski APPB(06)gq [boosted Kerr]; Witek et al PRD(10)-a1004 [in AdS spacetime].
@ Higher-dimensional: Headrick et al CQG(10) [static Kaluza-Klein black holes]; Wiseman a1107-ch [static and stationary].

Binary Black Holes > see numerical simulations of binary black holes.

Multiple Black Holes > s.a. binaries; models in numerical relativity; relativistic gravitating objects [two-body problem].
@ General references: Arbona et al PRD(98)gq/97; Brandt & Brügmann PRL(97)gq, gq/97-MG8 [punctures]; Loustó & Zlochower PRD(08)-a0710, Galaviz et al PRD(10)-a1004 [moving-puncture approach].
@ Apparent horizons: Anninos et al PRL(95)gq/94; Baumgarte et al PRD(96); Thornburg PRD(96); Schnetter gq/02.
@ Other horizons: Schnetter et al PRD(06)gq [dynamical]; Jaramillo et al PRD(07)gq/06 [isolated, boundary conditions implementation].
@ Horizon finders, trackers: Diener CQG(03) [full 3D]; Caveny et al PRD(03)gq; Thornburg LRR(07)gq/05; Lin & Novak CQG(07)gq [3D]; Cohen et al CQG(09)-a0809; Brooks et al GRG(18) [and Cartan invariants].
@ Related topics: Kidder et al PRD(00)gq [1D, pseudospectral collocation method]; Alcubierre & Brügmann PRD(01)gq/00, et al PRD(01)gq [excision]; Yo et al PRD(02)gq [stability].

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