Classical General Relativity  

In General > s.a. einstein's equation; history of gravitational physics.
* Motivation: (i) Inadequacy of concept of (global) inertial frames, and need to formulate a theory that does not have preferred reference frames; (ii) Inconsistency of Newtonian gravity with special relativity and indications that gravity can be associated with (geometrical) properties of spacetime; (iii) Equivalence principle.
* Idea: Gravity is a property of spacetime; Matter curves spacetime, and test bodies follow geodesics in the curved geometry.
* Formalism: The gravitational field is a metric tensor on a manifold with only a topology and differentiable structures as background; The theory comes out also if one looks for a self-interacting massless spin-2 field with stress-energy as source; But this will not work for quantum gravity, and has trouble with things like topology.
@ Early papers: Clifford PCPS(1876), 1885 [precursor, intuitive]; Einstein & Grossmann ZMP(13), ZMP(13), ZMP(14); Einstein SPAW(15), AdP(16), AdP(18); Schouten VKAA(18) [coordinate-free description].
@ Relations, "origin" of general relativity: von Borzeszkowski & Treder FP(96) [Mach's principle vs general relativity, Einstein-Grossmann and Einstein-Mayer theories]; Padmanabhan MPLA(02)ht, ASS(03)gq/02-conf [thermodynamics]; Deser GRG(10) [self-interacting spin-2 field]; Wiesendanger JModP(14)-a1308 [as the classical limit of a gauge theory of volume-preserving diffeomorphisms]; Barceló et al PRD(14)-a1401 [graviton self-interactions and the cosmological constant]; Hertzberg a1610, Hertzberg & Sandora a1702 [causality and quantum consistency]; > s.a. gravitational thermodynamics.

Approaches, Dynamical Aspects, and Effects > s.a. 3D general relativity.
* Idea: Study of the dynamics of the theory, including exact solutions and approximation methods, the initial value and canonical formulation, gravitational waves and radiation; And global properties of spacetime, including its topology, causal structure, and singularities.
@ Stability: Horowitz & Perry GRG(83); Abramo et al PLB(02)gq [with scalar].
@ Related topics: Gibbons FP(02) [maximal tension principle]; Padmanabhan IJMPD(04) [as elasticity of spacetime]; Jezierski & Kijowski gq/05 [unconstrained degrees of freedom]; Caticha AIP(05)gq [from statistical thermodynamical concepts]; Chruściel et al BAMS(10) [mathematical results]; Kobe & Srivastava a1309 [from Newtonian gravity]; Böhmer & Downes IJMPD(14)-a1405 [from continuum mechanics].
blue bullet Approaches: see canonical; formulations; initial-value formulation; modified versions [and limitations]; quantum gravity; semiclassical.
blue bullet Formalism, related areas: see action; causality; gauge transformations; geometry; numerical relativity; linearization; tensor decomposition.
blue bullet Phenomenology: see cosmology; experiments and tests; gravitating bodies; locality; phenomenology [including Newtonian limit]; radiation.
> Tools, techniques: see duality; energy-momentum; Fermat's Principle; observables; orbits of gravitating bodies; singularities; solutions.
> Applications: see GPS.

References
@ I: Durell 60; Gamow 62; Bondi 64; Russell 69; Geroch 78; Clarke 79; in Lightman 86, 58-69; Bergmann 87; Fang & Chu 87; Mook & Vargish 87; issue NatGeo(89)may; Gribbin NS(90)feb; Wheeler 90; Zee 90; Taylor & Wheeler 92; Wald 92; Will 93; Fritzsch 94; Hawking & Penrose 96; Dadhich gq/01-ln; Bassett & Edney 02; Vishveshwara 06; Cooperstock & Tieu 12; Egdall 14.
@ IIa: Schutz 03 [student's manual Scott 16]; Bertschinger & Taylor AJP(08)feb; Lopis & Tegmark a0804 + YouTube; Hraskó 11; Natário 11; Price AJP(16)aug [spacetime curvature].
@ IIb: Eddington 29; Lieber 36; Sciama 69; Frankel 79; Bose 80; Price AJP(82)apr; Naber 88; Kenyon 90; de Felice & Clarke 90; Hughston & Tod 91; d'Inverno 92; Harpaz 92; Mould 94; Martin 96; Sartori 96; Ludvigsen 99; Ellis & Williams 00; 't Hooft 00; Taylor & Wheeler 00; Kogut 01 [and special relativity]; Hartle 02; Foster & Nightingale 06; Hobson et al 06; Walecka 07; Ferraro 07; Ryder 09; Schutz 09 (student manual Scott 16); Cheng 10; Franklin 10; Narlikar 10; Lambourne 10; Grøn & Næss 11; Moore 12 [workbook, r AJP(13)apr, PT(14)may]; Steane 12; Gasperini 13 [and other theories]; Zee 13; Blecher 16; Böhmer 16.
@ II, cosmology emphasis: Burke 80; Dalarsson & Dalarsson 05; Grøn & Hervik 07.
@ II, other emphasis: Van Bladel 84 [practical]; Stephani 04 [formal]; Ohanian & Ruffini 13 [Newtonian, experiment]; Dray 14 [differential forms].
@ III: Bolton 21; Birkhoff 23; Eddington 37; Pauli 58; Fock 59; Born 62; Anderson 67; Robertson & Noonan 68; Synge 71; Møller 72; Weinberg 72; Hawking & Ellis 73; Misner, Thorne & Wheeler 73; Atwater 74; Papapetrou 74; Pathria 74; Adler et al 75; Bowler 76; Lord 76; Sachs & Wu 77; Mercier 79; Rindler 80; Treder et al 80; Wald 84; Straumann 84; Gasperini & de Sabbata 86; Martin 88; Stephani 90; Kopczyński & Trautman 91; Logunov 91; Stewart 91; Leite Lopes 94 [not recommended]; Tourrenc 97; Kriele 99; Carroll 03; Woodhouse 07; Hájíček 08; Padmanabhan 10; Sharan 10; DeWitt 11 [1971 lecture notes]; Das 11; Straumann 13; Frè 13 [and gravity]; Choquet-Bruhat 14.
@ III, cosmology emphasis: McVittie 65; Hakimi 98; Plebański & Krasiński 06 [and solutions]; Rindler 06; Grøn & Hervik 07.
@ III, astrophysics emphasis: Straumann 04; Lopis & Tegmark a0804; Poisson & Will 14.
@ III, other emphasis: Carmeli 77 [group theory]; Saleem & Rafique 92 [particle physics]; Ciufolini & Wheeler 95 [tests]; Carmeli 01 [gauge theory]; Poisson 04 [tools]; Khriplovich 05 [effects]; Choquet-Bruhat 09, Das & DeBenedictis 12 [mathematical]; Barrabès & Hogan 13 [gravitational waves, spinning particles, black holes]; in Thorne & Blandford 15.
@ Pedagogic features: Brill & Perisho AJP(68)feb [RL]; Roman AJP(86)feb; Morris & Thorne AJP(88)may; Francisco & Matsas AJP(89)apr [infinite straight string]; Adler & Brehme AJP(91)mar [uniform field]; Chandler S&E(94) [4D curved spacetime]; Rindler AJP(94)oct [general relativity before special relativity]; Levrini S&E(02); Drake AJP(06)jan-gq/05 [equivalence principle]; Hartle AJP(06)jan-gq/05 [approach]; Nandi et al EJP(06)gq/05 [orbits in general relativity and Newtonian gravity]; Wald AJP(06)jun-gq/05 [RL]; Kozyrev a0712; Kraus EJP(08) [visualizations]; Hobson AJP(08)jul; Le Tiec CQG(12)-a1202 [orbits and Killing vectors, covariance, etc]; Christensen & Moore PT(12)jun [teaching general relativity to undergraduates]; Dadhich CS-a1206; Lynden-Bell & Katz MNRAS(14)-a1312 [thought experiments with a cylinder]; Zahn & Kraus EJP(14)-a1405 [undergraduate level]; Mathur et al a1609 [merging black holes and gravitational waves in terms of introductory physics]; > s.a. Reference Frames.
@ Problems: Lightman et al 75; Bolotin & Tanatarov a1310 [cosmological horizons].
@ Short reviews: Bargmann RMP(57); Synge in(64); Trautman in(65); Thirring GRG(70); Ehlers in(73); Trautman in(73); Schücking GRG(76); Markov in(84); Canuto & Goldman in(94)-a1509; Ellis CQG(99)A; Damour a0704-proc; Iorio Univ(15)-a1504; Padmanabhan CS-a1512 [100 years]; Scheel & Thorne PU(14)-a1706 [geometrodynamics].
@ Lectures: Fock RMP(57); Feynman APP(63); Plebański pr(64); Geroch ln; Buchdahl 81; Carroll gq/97-ln [site]; van Holten FdP(97)gq [phenomenology]; Baez & Bunn AJP(05)jul-gq/01 [intro]; Popławski a0911 [and coupled fields]; Horowitz CQG(11)-a1010-GR19 [applications to condensed-matter physics]; Akhmedov a1601; Das Gupta a1604 [for pedestrians]; Menotti a1703 [field theory emphasis].
@ Other references: Sachs 82; Mészarós ASS(89); Chruściel et al BAMS-a1004 [recent mathematical advances]; Fay & Gautrias Scient(15)-a1502 [arXiv papers]; Coley & Wiltshire PS(17)-a1612 [the theory and its limits].
@ Collections: Witten 62; Kuper & Peres 71; Kilmister 73; Suppes 73; Esposito & Witten 77; Bonnor et al 85; Rindler & Trautman 87; Perjés 88; Matthews GRG(92); Chandrasekhar 93; Chruściel 97; Iyer & Bhawal 99; Ciufolini & Matzner 10; Ashtekar et al a1409, Ni 16, Vasconcellos 16 [centennial overviewa].

Conceptual / Philosophical Aspects > s.a. Interpretation of a Theory; spacetime and models [axioms].
@ Philosophical / axiomatic: Grünbaum 68; Graves 71; Angel 80; Torretti 83; Zahar 89; da Costa et al IJTP(90); Robinson 90; Sachs 93; Andréka et al a1101 [as a hierarchy of theories in the sense of logic, Vienna Circle approach]; Sid-Ahmed a1112; Andréka et al a1310 [complete axiom systems].
@ Conceptual: Bergmann in(71), in(90); Malament gq/05-in; Pitts SHPMP(06)gq/05 [absolute elements]; Barbour 06; Verozub a0911; Romero a1301 [ontology]; Pietschmann a1604 [general relativity as a partial return to Atistotle's "natural motion"]; > s.a. Counterfactuals; Covariance.

Online Resources > s.a. David Brown's GRwiki; Wikibooks index page.
@ I: Ute Kraus' Space-Time Travel site [visualization]; summary space(15)apr; Future Learn online course.
@ II / III: Sean Carroll's lecture notes; David Waite's modernrelativity; Marc Favata's gravitational-wave resources; Marcus Hanke's maths overview.

"Spacetime tells matter how to move; matter tells spacetime how to curve." — MTW


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