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].

@ __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];
> 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 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 (*λ*/*λ*_{Compton})^{2};
spacetime fluctuations (*λ*_{fundam}/*λ*)^{2}.

@ __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 a1706-IJGMP [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, a1406 [graviton self-interactions and the cosmological constant]; Hertzberg & Sandora a1702 [general relativity from causality]; Blasi & Maggiore 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]; > 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 a1706 [gravity could become repulsive in the future];
Ezquiaga & Zumalacárregui a1710 [neutron-star merger GW170817].

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