Classical General Relativity| Classical General Relativity |
In General
> s.a. einstein's equation; history of gravitational physics.
* Motivation: (i) Inadequacy of
the 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];
Kobe & Srivastava a1309 [from Newtonian gravity];
Barceló et al PRD(14)-a1401 [graviton self-interactions and the cosmological constant];
Hertzberg AHEP(17)-a1610,
Hertzberg & Sandora JHEP(17)-a1702 [causality and quantum consistency];
> s.a. gravitational thermodynamics.
@ Approaches: Sachs 82;
Mészarós ASS(89);
Padmanabhan IJMPD(04) [as elasticity of spacetime];
Caticha AIP(05)gq [from statistical thermodynamical concepts];
Böhmer & Downes IJMPD(14)-a1405 [from continuum mechanics];
Krasnov 20;
> s.a. formulations.
Approaches: see canonical; initial-value
formulation; modified versions [and limitations];
quantum gravity; semiclassical.
Dynamical Aspects, Results 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];
Jezierski & Kijowski gq/05 [unconstrained degrees of freedom];
Chruściel et al BAMS(10)-a1004 [recent mathematical results];
Coley GRG(19)-a1807 [mathematical, open problems].
Formalism, related areas: see action;
causality; gauge transformations;
geometry; numerical relativity;
linearization; tensor decomposition.
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;
Will & Yunes 20.
@ IIa: Schutz 03;
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;
Bambi 18;
Guidry 19;
Fleury 19;
Blecher 20;
Kanti Dey & Sen a2009 [intro].
@ 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;
Gray 19 [student guide];
Chruściel 19;
Natário 21 [mathematical].
@ 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;
Ferrari et al 21.
@ 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;
Soffel & Han 19 [applications];
Compère 19
[surface charges, 3D, asymptotic flatness, rotating black holes].
@ Pedagogic:
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 AJP(17)sep-a1609
[merging black holes and gravitational waves in terms of introductory physics];
Pössel a1901-conf [various kinds of models];
> 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].
@ Lecture notes: 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];
Compère & Fiorucci a1801 [surface changes, holographic features, BMS group];
Fleury a1902-ln;
Natário a2003 [mathematical];
Bilenky a2010.
@ Other references: Fay & Gautrias Scient(15)-a1502 [arXiv papers].
@ 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-in [ontology];
Pietschmann a1604
[general relativity as a partial return to Aristotle's "natural motion"];
Coley & Wiltshire PS(17)-a1612 [the theory and its limits];
Vassallo EJPS(20)-a1910
[dependence relations between between material and spatiotemporal structures];
Romano & Furnari 19 [foundations];
> s.a. Counterfactuals; Covariance.
Online Resources
> s.a. David Brown's Physics Unsimplified;
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
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 28 may 2021