Models in Numerical Relativity

Black Holes > 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: 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].
@ Spherically symmetric: Bona et al PRD(95)gq/94; Thornburg gq/99/PRD; Brewin gq/00-MG9; Ruíz et al 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 gq/06-PhD.
@ 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.
@ 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 gq/06 [punctures]; Boyle et al 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 ap/06-in [rev]; Tichy & Marronetti 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 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].
@ 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].

Gravitational Waves > s.a. collapse; [gravitational waves].
@ Plane waves: Bardeen & Buchman PRD(02)gq/01 [colliding].
@ From single black hole: Papadopoulos & Font PRD(99)gq/98 [method]; Gómez PRD(01)gq; Sopuerta & Laguna PRD(06)gq/05 [orbiting particle].
@ From binary inspiral: Baker et al PRL(01)gq, PRD(02)gq.
@ Related topics: Bishop et al PRD(96) [Cauchy + characteristic]; Kokubun PLA(98)gq [from Hénon-Heiles]; Sigalotti & Stark gq/99/CQG [non-axisymmetric]; New et al PRD(00)gq [adaptive mesh]; Garfinkle & Duncan PRD(01) [Brill waves]; Calabrese et al PRD(02)gq [KST stability]; Misner gq/05 [compactified, beyond ].

Quantum Gravity > s.a. regge calculus.
@ Lqg: Sabharwal & Khanna a0711 [lattice-refined models, cosmology and interior Schwarzschild].
@ Quantum cosmology: Berger GRG(88); Rosen et al CQG(06)gq [lqg, instabilities]; Laguna PRD(07)gq/06 [lqg and big bang].

Other Models / Systems / Theories > s.a. asymptotic flatness at spi and null infinity; fluid; phenomenology.
* Collapse: A standard procedure is to use excision techniques for the region where a singularity may develop.
@ Collapse: Shibata PTP(00)gq; Birukou et al PRD(02)gq [spherical scalar, any D and ]; Baiotti et al PRD(05) [ns to Kerr]; Dimmelmeier et al ap/06-in [stellar cores]; Baiotti & Rezzolla PRL(06)gq [without excision]; Shapiro a0711-in [black hole formation, rev].
@ Singularities: Berger gq/95, gq/95-ln; Berger et al gq/97-in [inhomogeneous], LRR(02)gq [rev].
@ With other fields: Barreto et al PRD(05) [Klein-Gordon, characteristic]; Zeller & Hiptmair CQG(06)gq [Einstein-Dirac, spherical symmetry].
@ Cosmology: Garfinkle PRD(99)gq [Gowdy]; Hern gq/00-PhD [inhomogeneous]; Anninos LRR(98)–LRR(01)gq.
@ Axisymmetric: Alcubierre et al IJMPD(01)gq/99; Frauendiener PRD(02)gq [stability], & Hein PRD(02); Choptuik et al CQG(03) [general code].
@ Compact binaries: Shibata PRD(99)gq [neutron stars]; Baumgarte & Shapiro PRP(03)gq/02; Marronetti CQG(05)gq [Hamiltonian relaxation]; Löffler et al gq/06 [black hole-neutron star].
@ Other models: Brügmann AdP(00)gq/99-in [3+1]; Watt & Misner gq/99 [scalar gravity]; Calabrese & Sarbach JMP(03)gq [linearized general relativity, boundary conditions].

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