Classical
General Relativity| Classical
General Relativity |
In General > s.a. einstein's
equation; history;
spacetime and models [axioms].
* 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.
* Question: Could we
say that in some sense the flat-space Newtonian form is replaced by a Gauss
form, as in the case of electromagnetism in curved spacetime?
@ 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-in
[thermodynamics]; > s.a. gravitational thermodynamics.
Approaches, Dynamical Aspects, and Effects > s.a. 3D
general relativity; action; causality; decomposition;
experiments and tests.
* 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 gq/05-in
[from statistical thermodynamical concepts].
> Approaches: see canonical; formulations; initial
value; linearized; matter
dynamics; modified; quantum; semiclassical.
> Applications:
see
cosmology; duality;
Fermat's Principle; GPS;
locality; phenomenology [including
Newtonian
limit]; radiation;
singularities.
> Results, techniques:
see energy-momentum; gauge
transformations; numerical; observables;
orbits of gravitating bodies; solutions.
References
@ I: Durell 60; Gamow 62; Bondi 64; Russell 69; Geroch 78; Clarke 79;
Bergmann 86; in Lightman 86, 58-69; Fang & Chu 87; Mook & Vargish
87; Will 88; National Geographic (89)may; Gribbin NS(90)feb;
Wheeler 90; Zee 90; Taylor & Wheeler
92; Wald 92; Fritsch 94; Hawking & Penrose 96; Dadhich gq/01-ln;
Bassett & Edney 02; Vishveshwara 06.
@ IIa: Schutz 03; Bertschinger & Taylor AJP(08)feb;
Lopis & Tegmark a0804 +
YouTube.
@ II: 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; Grøn & Næss
02; Cheng 05; Foster & Nightingale 06; Hobson
et al 06; Walecka 07;
Ryder 09;
Schutz 09.
@ II, cosmology emphasis:
Burke
80; Dalarsson & Dalarsson 05; Grøn & Hervik 07.
@ II, other emphasis: Van Bladel 84 [practical]; Ohanian & Ruffini
94 [Newtonian, experiment]; Stephani 04 [formal].
@ III: Bolton 21; Birkhoof 23; Eddington 37; Pauli 58; Fock 59; Born
62; Anderson 67; Robertson & Noonan 68; Synge 71; Möller
72; Weinberg 72; Hawking & Ellis 73; Misner, Thorne & Wheeler 73;
Atwater 74; Papapetrou 74; Pathria 74; Adler et al 75; Lightman et al 75; Bowler
76;
Lord 76; Sachs & Wu 77; Mercier 79; Rindler 80; Treder et al 80; Wald
84; Straumann 85; Gasperini & de Sabbata 86;
Martin 88; Stephani 90; Kopczynski & Trautman
91; Logunov 91; Stewart 91; Leite Lopes 94 [not recommended]; Tourrenc 97;
Kriele 99; Carroll 03; Woodhouse 07; Hájícek 08;
Padmanabhan 09.
@
III, cosmology emphasis: McVittie 65; Hakimi 98; Plebanski & Krasinski
06 [and solutions]; Rindler 06.
@ III, other emphasis: Carmeli 77 [group
theory]; Saleem & Rafique 92 [particle physics]; Ciufolini & Wheeler
95 [tests]; Poisson 04 [tools]; Straumann 04 [astrophysics];
Khriplovich 05 [effects]; Lopis & Tegmark a0804 [astrophysics];
Choquet-Bruhat 09 [mathematical].
@ 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]; 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]; Wald AJP(06)jun-RL-gq/05;
Kozyrev a0712;
Kraus EJP(08)
[visualizations]; Hobson AJP(08)jul;
> s.a. Reference Frames.
@ 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); Ellis CQG(99)A;
Damour a0704-in.
@ Lectures: Fock RMP(57);
Feynman APP(63); Plebanski pr(64);
Geroch; Buchdahl 81; Carroll gq/97-ln;
van Holten FdP(97)gq [phenomenology];
Baez & Bunn AJP(05)jul-gq/01 [intro];
Poplawski a0911 [and coupled fields].
@ Other references: M Sachs 82; Mészarós ASS(89).
@ Collections: Witten 62; Kuper & Peres 71; Kilmister 73; Suppes 73;
Esposito & Witten 75; Bonnor et al 85; Rindler & Trautman 87; Perjés
88; Matthews GRG(92);
Chandrasekhar 93; Chrusciel 97; Iyer & Bhawal 99.
Conceptual / Philosophical Aspects > s.a. Interpretation
of a Theory.
@ Philosophical / axiomatic: Grünbaum 68; Graves 71; Angel
80; Torretti 83; Zahar 89; da Costa et al IJTP(90);
E Robinson 90; Sachs 93.
@ Conceptual: Bergmann in(71), in(90);
Malament gq/05-in;
Pitts SHPMP(06)gq/05 [absolute
elements]; Barbour 06; > s.a. Covariance.
Online Resources > see David Brown's GRwiki; Sean Carroll's lecture notes; Ute Kraus' Space-Time Travel site; Wikibooks index page.
main page – abbreviations – journals – comments – other
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send feedback and suggestions to bombelli at olemiss.edu – modified 2
nov 2009