Gravitation |

**In General**
> s.a. newtonian gravity and modifications;
gravitational phenomenology.

* __History, I__: The first systematic studies
were carried out by Galileo (XVI century), or maybe by Riccioli; Hooke suggested that gravity
plays a role in celestial motions, but the first precise description is Newton's (1665).

* __History, II__: 1915, The equivalence principle,
Einstein's theory of general relativity, gravity as geometry; 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; Alternative gravity theories.

* __History, III__: Various precursors are XX
century proposals of higher-dimensional gravity, discrete theories, etc; 1990s, Beginning
of a systematic study of phenomenology of higher-dimensional models; Quantum gravity?

* __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.

@ __Intros and textbooks__: Schutz 03 [II];
Olmo a1112-ch [intro];
Gasperini 13 [II, and other interactions];
Girifalco 14 [I];
Fleury a1902-ln [IIb].

@ __General references__: Cartan ENS(23),
ENS(24), ENS(25);
Mann gq/98-GR15;
Aguirre et al CQG(01)hp [and astrophysics];
Deser IJMPA(02)ht/01 [rev];
Sotiriou et al IJMPD(08)-a0707 [no-progress report];
Krasnov MPLA(07)-a0711 [non-metric theories];
Sotiriou PhD(07)-a0712 [theory and phenomenology];
Zee IJMPA(08)-a0805-conf [rambling talk];
Padmanabhan FP(08) [and the equivalence principle];
Percacci PoS-a0910
[particle-physics perspective, gauge and renormalization];
Ananth IJMPD(10) [and Yang-Mills theory];
Bertolami a1112-talk;
Starkman PTRS(11)-a1201 [and cosmology];
Frampton & Karl a1304 [at very short distances];
Trippe ZfN(14)-a1401 [the missing mass problem and the need for a new theory];
Papini MPLA(14) [covariance and gauge invariance];
Capozziello & Lambiase a1409-conf [open problems];
Lobo JPCS(15)-a1412 [dark matter, dark energy and modified gravity];
Strominger a1703-ln [infrared structure].

@ __History__: Synge et al PRS(62),
Hoyle et al PRS(62) [status];
Gondhalekar 01;
Kumar & Suresh gq/06;
Graney PT(12)sep [Riccioli];
Pitts a1907-ch;
> s.a. history of relativistic physics.

@ __Speculations, origin of gravity__: Mazur APPB(96)ht;
Wootters FP(03) [from simple assumptions];
Amelino-Camelia et al IJMPD(15)-a1505-GRF [breakdown of conformal invariance];
Sels & Wouters JPCS(17)-a1602 [from mutual information in many-body quantum systems];
Altamirano et al NJP(17)-a1605 [from repeated quantum measurements];
Khosravi PRD(16)-a1606 [from ensenble average of all theoretically consistent models];
> s.a. emergent gravity; entropic gravity;
phenomenology of entanglement; dynamical
wave-function collapse.

@ __Gravity as a universal force__: Dieks Syn(87) [Reichenbach and Grünbaum];
Dadhich gq/04,
gq/04-proc [universality??].

@ __Gravity as geometry__: Giesel et al PRD(12)-a1202 [based tensorial geometries other than Lorentzian geometries];
Capozziello et al IJGMP(12)-a1202 [physical foundations, Ehlers-Pirani-Schild approach];
Capozziello et al IJGMP(14)-a1401 [symmetries and affine structure].

> __And other areas of physics__:
see modified quantum theory.

> __Online resources__: see Internet Encyclopedia of Science
pages;
Verlinde, Wilczek and Mersini-Houghton debate.

**Types of Theories**
s.a. theories of gravity [including higher-spin, vector, vector-tensor, ... theories].

* __General idea__: 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; It can be fundamental or 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__: General relativity
(or another covariant gravity theory) is intrinsically non-linear because it must be
self-interacting or "charged" if it is to interact consistently with matter
via its stress tensors; This can be shown by bootstrapping the theory starting from
any background; Of all the purely metrical theories, i.e., *L* = *L*(*g*,
∂*g*, ∂∂*g*, *φ*, ∂*φ*), only general
relativity with arbitrary matter, i.e., *L* = |*g*|^{1/2}
*R* + *L*(*g*, *φ*, ∂*φ*), gives second-order
equations in *g* (and is linear in ∂∂*g*), and not fourth-order; A
large class of these theories are "dynamically equivalent" to general relativity.

* __Sources of corrections__:
A graviton mass gives corrections of order \((\lambda/\lambda^{~}_{\rm Compton})^2\),
spacetime fluctuations corrections of order \((\lambda^{~}_{\rm fundam})^2/\lambda\).

@ __General references__:
Weyl AJM(44) [as a linear field theory];
Deser GRG(70)gq/04 [need for non-linearity];
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 [universality of Ricci-squared theories];
Knox SHPMP(11)
[empirically equivalent theories and underdetermination];
Fabris & Velten a1501-proc [neo-Newtonian theories];
Licata et al IJGMP(17)-a1706 [approach based on the covariant derivative commutator algebra];
Clifton & Sanghai a1803 [parameterizations of alternative theories].

@ __Non-relativistic theories__: Kocharyan PRD(09)-a0905;
Greenwald et al JCAP(10)-a1010 [compact objects and solar-system tests];
> s.a. hořava-lifshitz gravity; lorentz-symmetry
violations; newtonian gravity.

@ __As a spin-2 field theory in Minkowski space__:
Barceló et al PRD(14)-a1401,
AP(18)-a1406 [graviton self-interactions and the cosmological constant];
Hertzberg & Sandora JHEP(17)-a1702 [general relativity from causality];
Blasi & Maggiore EPJC(17)-a1706 [and Fierz-Pauli theory];
> s.a. formulations of general relativity.

@ __Other theories__: Moffat EPJP(11)-a1008 [ultraviolet complete];
Letelier a1105
[non-covariant, with *L* = |*g*|^{ω} *R*];
Greenberger FP(12) [Tic-Tac-Toe theory, negative masses and the equivalence principle];
Pani et al PRD(13)-a1306 [with auxiliary fields];
Salvio & Strumia JHEP(14)-a1403 [agravity, theory without scales];
Markou et al a1811 [vierbein, antisymmetric tensor];
Jokela et al a1901
[gravity dual to a system of (2+1)-dimensional layers];
> s.a. differential geometry.

__General relativity and related theories__: see general relativity,
its formulations and variants [including infrared modifications].

__Modified theories__: 2D and 3D theories;
higher-dimensional gravity; higher-order theories;
modified gravity; non-local theories.

__Other types__: see ads-cft correspondence [gauge/gravity
duality]; Disformal Gravity; emergent gravity [including
analog gravity]; entropic gravity; parity-violating theories;
Projective Relativity;
Screened Modified Gravity.

**Phenomenology** > s.a. Antigravity [repulsive component];
black holes; gravitational phenomenology;
tests of general relativity.

@ __References__: Fischbach & Talmadge 99 [non-Newtonian];
Capozziello & Faraoni 11 [cosmology and astrophysics];
Linder JPCS(14)-a1201;
Dupré a1403
[tidal acceleration and the structure of local gravity theories];
Di Virgilio et al proc(17)-a1702 [rev];
Albarran et al EPJC(18)-a1706 [gravity could become repulsive in the future];
Ezquiaga & Zumalacárregui a1710 [neutron-star merger GW170817].

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