Phenomenology and Tests of Gravity| 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 gab ≈ η − 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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