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.

Single Black Holes
@ 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]; Karkowski APPB(06)gq [boosted Kerr]; Tichy a0911 [long-term evolution, pseudospectral methods].
@ From particle collisions: Choptuik & Pretorius a0908 [ultra-relativistic].
@ 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].
@ 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.
@ Perturbations: Krivan et al PRD(97) [Kerr, effects]; Brandt et al gq/97-in; 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.

Binary and Multiple Black Holes
* Rem: Extreme-mass-ratio cases are more difficult to handle numerically than equal-mass black holes, although simpler in perturbation theory.
* Kicks: Numerical results have shown that asymmetric gravitational wave emission provides a net kick to the black hole produced as a result of a merger; This kick appears to be sufficient to expel it from a globular cluster or small galaxy, but not from a large galaxy.
@ Binaries: Baker et al PRD(02) [Lazarus project]; Damour et al PRD(02)gq; Khanna PRD(02)gq; Brügmann et al PRL(04)gq/03; Zlochower et al PRD(05)gq [4th-order accuracy]; Pretorius PRL(05)gq; Diener et al PRL(06)gq/05 [last orbit]; Pretorius CQG(06)gq [generalized harmonic coordinates]; Hannam et al PRL(07)gq/06 [punctures]; Boyle et al PRD(08)-a0804 [gravitational-wave energy loss].
@ Binaries, data: Berti et al PRD(06) [eccentricity in data]; Dennison et al PRD(06) [approximate].
@ Binaries, colliding: Brandt et al gq/97-MG8; Anninos & Brandt PRL(98)gq; Seidel gq/98-GR15; Brügmann IJMPD(99) [3+1]; Gómez et al PRD(01)gq/00; Dain PRD(01)gq; Husa et al gq/01-MG9; Gourgoulhon et al IJMPA(02)gq-in [last orbit]; Khanna PRD(02)gq [parallel spins]; Campanelli et al PRD(06)gq; news pw(06)apr; Centrella AIP-ap/06 [rev]; Tichy & Marronetti PRD(08)-a0807 [final mass and spin].
@ Several black holes: Arbona et al PRD(98)gq/97; Brandt & Brügmann PRL(97)gq, gq/97-MG8 [punctures]; Loustó & Zlochower PRD(08)-a0710 [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, bc 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.
@ 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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