Numerical General Relativity

In General
* Motivation: Make realistic astrophysical predictions; Use to look for chaos (the first positive claims were wrong because the constraints were not preserved, and error propagation simulated negative energy density).
* History, status: 1960s, First attempts at solving a binary black hole spacetime by Hahn and Lindquist; 1976, B DeWitt coins the expression "numerical relativity"; 1989, Some 3D problems, like collapse and gravitational wave production, can be tackled; 1992, First qualitatively new solution found by numerical methods, Choptuik's critical collapse; 1994-1999, Binary-black-hole grand challenge; Still relatively few 3D problems done; Also, better understanding of the convergence of Regge calculus, theoretically, but in practice method for Regge calculus not as developed (choosing initial data involves solving elliptical differential equations); 2005, F Pretorius breakthrough and stable simulation of black-hole inspiral and merger; 2009, About 11 groups worldwide can now do full merger simulations; New results have been obtained (gravitational recoil "kicks", black-hole triplets, gravitational-wave production); Gravity is in the process of becoming data-driven.
* Data: One way of handling the fact that the region is finite is to give data on a finite spacelike region, and then free data on the outgoing light front from its boundary.

Related topics: see issues and methods; models in numerical relativity [collapse, binaries, cosmology, astrophysics].

Gauge and Coordinate Choices > s.a. coordinates; gauge choices.
* Idea: It looks like the best gauge choices are dynamical ones.
@ Choices and effects: Alcubierre & Massó PRD(98)gq/97 [gauge problems]; Garfinkle & Gundlach CQG(99)gq [approximate Killing vector field]; Garfinkle PRD(02)gq/01 [harmonic coordinates]; Reimann et al PRD(05)gq/04, Alcubierre CQG(05)gq [gauge shocks].
@ BCT gauge (minimal strain equations): Brady et al; Gonçalves PRD(00)gq/99; Garfinkle et al CQG(00)gq.
@ Special cases: Gentle et al PRD(01)gq/00 [constant K and black holes].

Constraints > s.a. Symplectic Integrators.
* Idea: Due to finite precision errors, constraints in numerical relativity are never exactly satisfied, so one can solve them initially and then simply monitor them as a check on the evolution (unconstrained evolution), or somehow enforce them as part of the evolution; 2008, Recent simulations use initial data generated by constraint solvers that differ by the amount of gravitational radiation they include in the initial configuration.
@ General references: Detweiler PRD(87); Cook LRR(00)gq; Tiglio gq/03 [control]; Fiske PRD(04)gq/03 [as attractors]; Gentle et al CQG(04)gq/03 [as evolution equations]; Baumgarte PRD(12)-a1202 [Hamiltonian constraint, alternative approach]; Okawa IJMPA(13)-a1308-ln [elliptic differential equations].
@ And boundary conditions: Calabrese et al PRD(02)gq/01; Calabrese & Sarbach JMP(03) [ill-posed]; Sarbach & Tiglio JHDE(05)gq/04; Kidder et al PRD(05)gq/04; Rinne et al CQG(07)-a0704 [comparison of methods]; > s.a. methods in numerical relativity.
@ Enforcement and violations: Siebel & Hübner PRD(01)gq [effects of enforcement]; Lindblom & Scheel PRD(02)gq [violations and stability]; Berger GRG(06)gq/04-fs; Matzner PRD(05)gq/04 [hyperbolicity and constrained evolution]; Marronetti CQG(05)gq [Hamiltonian relaxation], CQG(06)gq/05, gq/06-MGXI [constraint relaxation]; Paschalidis et al PRD(07) [well-posed evolution].

References
@ Books and collections of papers: Centrella ed-86; Evans et al ed-88; d'Inverno 92; Hehl et al ed-96; issue CQG(06)#16, CQG(07)#12, CQG(09)#11; Alcubierre 08; Bona et al 09 [and relativistic astrophysics]; Baumgarte & Shapiro 10; issue CQG(10)#11; Shibata 16; Baumgarte & Shapiro 21 [from scratch].
@ Reviews: Lehner CQG(01)gq, gq/02-GR16; van Putten gq/02-conf; Rezzolla in(14)-a1303-proc; Cardoso et al LRR(15)-a1409 [fully non-linear evolutions and perturbative approaches, applications to new physics]; Garfinkle RPP(16)-a1606 [applications beyond astrophysics]; Tichy RPP(17)-a1610 [initial-value problem]; Palenzuela FASS-a2008 [intro].
@ Other theories of gravity: Torsello et al CQG(20)a1904 [bimetric gravity, covariant BSSN formulation].
@ Other general references: Hobill & Smarr in(89); Choptuik et al CQG(92) [spherical, scalar + gravity, 2 codes]; Anninos et al PW(96) [II, black holes]; Alcubierre gq/04-GR17; Shapiro PTPS(06)gq/05-proc [rev]; Andersson CQG(06)gq [and mathematical relativity]; Babiuc et AppleswithApples CQG(08)-a0709 [standard testbeds]; Sekiguchi CQG(10)-a1009 [taking microphysics into account]; Cardoso et al CQG(12)-a1201 [NR/HEP Workshop summary]; Zilhão a1301-PhD [extensions to higher dimensions, non-asymptotically flat spacetimes and Einstein-Maxwell theory].
@ Computational aspects: Suen gq/99-rp [and TeraFlop machines]; Löffler et al CQG(12)-a1111, Zilhão & Löffler IJMPA(13)-a1305-ln, Choustikov a2011 [Einstein Toolkit, based on Cactus].

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