Phenomenology and Tests of Gravity  

Post-Newtonian (PN) Approximation / Corrections > s.a. higher-order gravity; newtonian gravity and tests; tests of general relativity.
* Idea: The post-Newtonian approximation is a method for solving Einstein's field equation for physical systems in which motions are slow compared to c and gravitational fields are weak (Tab is dominated by T00 = ρ, small momentum and stresses); The metric and geodesic equation can then be approximated by

g00 = −1 − 2φ/c2 + O(v/c) ,    or    gabη − 2φ 1 ,    and    d2xa / dt2 = −Γa00 = −∂aφ ;

introducing the lowest T0a corrections yields gravitomagnetism.
* And Newtonian force: The source of the Newtonian-like force is T 00 + Tii; > s.a. force.
* Infinite-c limit: One obtains the newton-cartan theory; > s.a. Ehlers' Frame Theory.
@ Newtonian limit: in Wald 84, §4.4; Gruber et al AJP(88)mar; Stacey & Tuck PW(88)dec; Frittelli & Reula CMP(94)gq/95; Schäfer GRG(09) [canonical dynamics approach]; Cederbaum PhD-a1201 [for static isolated systems]; Kopeikin a1212-conf [in an expanding FLRW universe]; Jaén & Molina a1505 [and Painlevé-Gullstrand synchronization]; Buchert & Mädler GRG-a1910 [on Ehlers' 1981 paper].
@ Post-Newtonian approximation: Schutz in(84); Frisch AJP(90)apr; Asada & Futamase PTPS(97)gq/98; Arminjon NCB(01)gq [methods]; Kaplan et al PRD(09) [in Maxwell-like form]; Tichy & Flanagan PRD(11)-a1101 [1st-order, covariant formulation]; Will PNAS(11)-a1102 [effectiveness]; Cho a1911 [rev].
@ Related topics: Dadhich gq/97 ["minimally curved spacetime"]; Hitzer & Dehnen IJTP(97)gq/98 [gauge for weak field]; Dautcourt APPB(98)gq [ultrarelativistic limit]; Nowakowski IJMPD(01)gq/00 [with cosmological constant]; Grumiller PRL(10)-a1011 [at large distances]; Hernández Ent(12)-a1203 [phase diagram with critical acceleration scale]; > s.a. dynamics of gravitating bodies; gravitomagnetism; PPN Formalism.

Effects on Waves > s.a. dirac fields; gravitational redshift and retardation; lensing and light bending; polarization; wave tails.
* Geometric optics approximation: To 0-th order in wavelength or inverse frequency, light rays are null geodesics, and the stress-energy tensor of the field has the form of that of a null fluid.
@ Geometric optics: Ehlers ZN(67); Anile JMP(76); in Misner et al 73; Mashhoon PLA(87); in Schneider et al 92; in Nolan gq/96.
@ Light bending: Ehlers & Rindler GRG(97) [local vs global]; Guadagnini PLB(02)gq [polarization change].
@ Bending, plane waves: Samuel CQG(04)gq/02 [Earth's field].
@ Birefringence: Solanki & Haugan PRD(96); Preuß PhD(02)gq/03 [metric-affine theory]; Preuss et al PRD(05)gq [Poincaré gauge theory]; Duval et al a1812 [from lensing in Schwarzschild spacetime].
@ Related topics: Peters PRD(74), Evans et al AJP(01)oct-gq [index of refraction in curved spacetime]; Barrabès & Haugan 04 [impulsive signals]; Papini gq/03-in [inertial + gravitational effects on wave equations]; Mackay et al NJP(05) [negative phase velocity]; San Miguel et al QCG(09) [curvature of light wavefront]; > s.a. light [gravitational field]; metric matching; Poynting Vector.

Effects on Matter > s.a. gravity theories; gravitating bodies and fields; spacetime [measurements].
* Particle properties: Some theories predict a graviton mass, and more polarizations for gravitational waves.
@ General topics: Thorne in(84) [non-linear]; Mashhoon PLA(92) [re strength of gravitational field]; Consoli & Costanzo a0710 [evidence for flat spacetime gravity?]; Álvarez & Vidal JHEP(09)-a0907 [stability, with a cosmological constant]; Pachón & Dubeibe CQG(11) [atoms in general relativity and the Landé factor]; Freidel CQG(15)-a1312 [correspondence between gravity in finite regions and non-equilibrium thermodynamics]; Anastopoulos et al a2103 [macroscopic quantum systems].
@ Effects on gravitating bodies: Guéron & Mosna PRD(07) [slowdown of infall from oscillations]; > s.a. motion of gravitating bodies.
@ Effects on particles: Fischer a0805 [gravitational viscosity]; Konno & Takahashi PRD(12)-a1201 [non-inertial and gravitational effects on quantum states]; > s.a. chaotic motion; motion of test bodies; tests of general relativity with orbits.
> Related phenomena: see aharonov-bohm effect; atomic physics [Stark effect]; black-hole phenomenology; electricity [Coulomb's law]; gravitational collapse, radiation, Precession, thermodynamics; tests of general relativity [including GPS].
> Puzzles / anomalies: see Allais Effect; anomalous acceleration.

Cosmological and Astrophysical Effects > s.a. astrophysical and cosmological tests; relativistic cosmology.
* Gravitational slip: A post-general relativity cosmological parameter characterizing the degree of departure of the laws of gravitation from general relativity on cosmological scales.
@ General references: Lamey & Obermair gq/05 [local/global, irreversibility]; Cook a0902 [space dilatation]; Chakrabarti et al GRG(11)-a0908; Lane et al MNRAS(09)-a0908 [velocity dispersion in globular clusters]; Tsagas PRD(10) [effect of Weyl tensor on Maxwell fields]; Lynden-Bell & Katz MNRAS(14)-a1312
@ Gravitational slip: Daniel et al PRD(09)-a0901; Sawicki et al PRD(17)-a1612 [and propagation of gravitational waves].
@ Effects of modified gravity: Jain & Zhang PRD(08)-a0709 [tests]; Hernández et al A&A(10)-a0904 [MOND-modelled empirical gravity law]; Brax et al JCAP(10)-a0912 [Yukawa-type force]; Boyarsky & Ruchayskiy PLB(11)-a1001 [dark-matter halos]; Davis et al PRD(12)-a1102 [stellar evolution and galaxy brightness]; Brax & Davis JCAP(15)-a1506 [variation of constants and spectroscopic velocities in various modified gravity theories].
> Related phenomena: see astrophysics; chaos; global geometry and topology.
> Specific theories: see bigravity; branes; higher-order gravity; Metric-Affine Gravity; modified general relativity; scalar-tensor theories; supergravity.

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