Theories of Gravitation  

In General > s.a. 2D and 3D theories; modified general relativity; newtonian gravity and modifications; phenomenology.
* History: The first systematic studies were by Galileo (XVI century); Hooke suggested that it plays a role in celestial motions, but the first precise description is Newton's (1665); 1920s, Cartan analyzed the geometric structure of Newtonian gravity (in terms of a degenerate non-dynamical metric) and general relativity, and introduced the concept of torsion; A general framework is Ehler's Frame Theory; 1990s, Beginning of a systematic study of phenomenology of higher-dimensional models.
* Strength: When we jump off a ledge, gravity takes over, but what happens when we hit the ground below?
* Motivation to look for new theories: Galactic rotation curves (unless explained by dark matter) and cosmological expansion acceleration (unless explained by dark energy); Eötvös-type experiments; Anomalous spacecraft acceleration; Search for theory of quantum gravity and quantum corrections to classical gravity.
@ General references: Cartan ENS(23), ENS(24), ENS(25); Mann gq/98-in; Mazur APPB(96)ht [speculative]; Fischbach & Talmadge 99; Aguirre et al CQG(01)hp [and astrophysics]; Deser IJMPA(02)ht/01 [rev]; Schutz 03 [II]; Wootters FP(03) [gravity from simple assumptions]; Sotiriou et al IJMPD(08)-a0707 [no-progress report]; Krasnov MPLA(07)-a0711 [non-metric theories]; Sotiriou a0712-PhD [theory and phenomenology]; Zee IJMPA(08)-in-a0805 [rambling talk]; Padmanabhan FP(08) [and the equivalence principle]; Percacci a0910-ln [particle-physics perspective, gauge and renormalization].
@ History: Synge et al PRS(62), Hoyle et al PRS(62) [status]; Gondhalekar 01; Kumar & Suresh gq/06.
@ Gravity as a universal force: Dieks Syn(87) [Reichenbach and Grünbaum]; Dadhich gq/04, gq/04-in [universality??].
@ Gravity as emergent / non-fundamental: Barceló et al IJMPD(01)gq; Volovik 03 [low-energy behavior of Fermi liquids]; Padmanabhan AIP(07)-a0706-in, IJMPD(08) [conceptual]; Sernelius IJMPA(09)-a0804 [as Casimir interaction]; Padmanabhan ASL-a0807-in [from theory of null vectors, and cosmological constant]; Girelli et al PRD(09)-a0806; Jannes a0810-in [condensed-matter-type collective excitations]; Kober PRD(09)-a0812 [from fundamental spinors]; Jenkins a0904-GRF [difficulties]; Lee IJMPA(09)gq/06 [from interacting simplices]; Liberati et al a0909-in [analog models]; Padmanabhan a0910-in; Consoli CQG(09) [Bose condensate]; > s.a. approaches to quantum gravity [including internal relativity]; Induced Gravity; models for spacetime; non-commutative gravity; non-commutative gauge theories [electromagnetism].
@ And cosmology: Mannheim PPNP(06)ap/05; Lobo a0807-in; Grishchuk SSR-a0903; Darabi a0907 [Machian model of gravity at galactic scales].
@ Repulsive component: Mannheim FP(00)gq; Matilsky ap/00/ApJL.
> Online resources: Internet Encyclopedia of Science pages.

Various Theories > s.a. differential geometry; higher-dimensional gravity; newton-cartan theory; Projective Relativity.
* Types: The first one in the modern sense was Newtonian gravity (originated in the 1660s, formulated in terms of action at a distance); The modern ones are usually geometrically formulated, as relativistic field theories; Can be fundamental of derived from other theories (induced gravity, AdS-cft, ...); Phenomenologically, the best motivated ones are scalar-tensor theories.
* Frameworks: The main ones in which various theories can be included and compared are the Dicke framework [@ in Dicke 64], and the PPN framework [which only treats conservative aspects, and does not include radiation]; There is also a Post-Keplerian framework, and Goldberger's & Rothstein's 2004 NRGR ("Non-Relativistic General Relativity", an unfortunate name) [this does include radiation].
* Results: Of all the purely metrical theories, i.e., L = L(g, g, g, , ), only general relativity with arbitrary matter, i.e., L = |g|1/2 R + L(g, , ), gives second-order equations in g (and is linear in g), and not fourth-order; Furthermore, a large class of these theories are "dynamically equivalent" to general relativity.
* Sources of corrections: A graviton mass gives corrections of order (/Compton)2; spacetime fluctuations (fundam/)2.
@ References: Ferraris & Kijowski GRG(82); Ferraris et al in-GR11; Ferraris et al CQG(88) + comment Brans CQG(88) + reply Ferraris et al CQG(90); Borowiec et al CQG(98)gq/96 [Ricci squared], gq/00-in [fourth-order].
@ Non-relativistic theories: Kocharyan PRD(09)-a0905; > s.a. Horava-Lifshitz Gravity; lorentz-symmetry violations; newtonian gravity.
> Phenomenology: see Antigravity; black holes; gravitational phenomenology; tests of general relativity.

Other Metric Theories > s.a. actions and formulations of general relativity [embedding]; higher-order and modified theories [non-local].
@ General references: Gupta RMP(57); in Schrödinger 63; De Alfaro et al NCB(80); Mann CQG(84), CQG(89).
@ With preferred frame: Petry GRG(79); Schmelzer gq/96, gq/96; Kohler GRG(00)gq/99 [semi-teleparallel]; Eling & Jacobson PRD(04)gq/03 [dynamical]; > s.a. Ether, modified lorentz symmetry.
@ Massive gravity: Logunov TMP(94); Damour et al PRD(03)ht/02 [spherical symmetry]; Porrati ht/04-in [in anti-de Sitter and Minkowski]; Chen ap/05 [with antigravity for fermions]; Berezhiani et al JHEP(08)-a0803; Babichev et al PRL(09)-a0907 [Schwarzschild solution]; de Rham a0910 [non-linear realization]; > s.a. graviton; interactions [instantaneous].
@ Variable c: Magueijo PRD(00)gq, PRD(01)ap/00; > s.a. relativistic cosmology; variation of constants.
@ Scale-invariant: Kelleher CQG(04)gq/03, CQG(04)gq/03, PhD(03)gq [spatially]; Verma gq/05; Darabi a0907; > s.a. Conformal Gravity.
@ Other: Visser GRG(98)gq/97 [background metric]; Drummond gq/99 [variable lightcone]; Anderson gq/99 [cosmological stress tensor]; Magueijo & Smolin CQG(04)gq/03 ["doubly general"]; Jackiw & Pi PRD(03)gq [with Chern-Simons-like term]; Schuller & Wohlfarth NPB(04) [with bounds on sectional curvatures]; Roscoe ap/04/CQG [relational]; Deser CQG(06)gq [with non-degeneracy as field equation]; > s.a. born-infeld theory; finsler geometry; modified lorentz symmetry.
> With additional variables: see bimetric theories; Metric-Affine Theories; scalar-tensor theories; TeVeS.

Other Variables > s.a. canonical general relativity; einstein-cartan theory; Non-Symmetric Gravity; Scalar Theory; string theory.
@ Connection: Jakubiec & Kijowski JMP(89) [non-symmetric]; Aldrovandi et al gq/98v1; Alexandrov CQG(00)gq [SO(4,C) lqg].
@ Deformed: Chamseddine PLB(01)ht/00; > s.a. non-commutative gravity.
@ W-gravity: Hull CMP(93)ht/92; Castro JGP(00)ht/98 [from Fedosov quantization]; Abreu et al PRD(02)ht.
@ Spinors, Dirac operator: Landi & Rovelli PRL(97)gq/96, MPLA(98)gq/97, Landi gq/99-in [eigenvalues]; Holfter & Paschke ht/02 [moduli space, path integrals]; Hebecker & Wetterich PLB(03)ht [higher-dimensional], Wetterich PRD(04)ht/03; Moffat gq/03 [and cosmological constant]; Novello gq/06 [gravity as effective theory].
@ Vectors: Goenner & Leclerc gq/00/PRD [+ scalar]; Moffat JCAP(06)gq/05 [scalar-tensor-vector]; Borodikhin a0802 [and solar system tests]; Jiménez & Maroto JCAP(09)-a0811 [vector-tensor theories], PRD(09)-a0905 [cosmological evolution]; Svidzinsky a0904 [vector theory, no black holes]; Guendelman a0911 [vector field giving dynamical time]; Faddeev a0911 [10 vectors].
@ People with their own theories: Havel 03.
@ As non-linear spin-2 field: Novello & De Lorenci MPLA(95); Sokolowski IGJMP(07)gq [and gravitational energy].
@ Other: Alvarez et al PLB(92), PLB(93) [2-point distance]; Hammond GRG(99) [2-form, torsion]; Østvang gq/01-PhD, G&C(05)gq/01, G&C(07)gq/02 [quasi-metric gravity]; Mensky G&C(02)gq [in terms of paths in Minkowski]; Bengtsson MPLA(07)gq; Fernández & Rodrigues a0909 [distorted Lorentz vacuum].
> Other: see Affine Gravity; Barker's Theory; forms [volume form]; Designer Gravity; Gauge Theory; Gauss-Bonnet Gravity; Ghost Fields; Hypergravity; lattice gravity [and regge calculus]; lorentzian geometry [analogs]; Matroids; Relativistic Theory of Gravitation; Supermanifolds; Topological Gravity; types of field theories [daor fields]; unified theories [including Weyl's]; Unparticles [ungravity]; Yilmaz Theory.

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