Modified
Newtonian Dynamics (MOND) |

**In General** > s.a. variation of constants.

* __Idea__: At accelerations
below a certain value *a*_{0} (*g* = ∇Φ <
*a*_{0}),
Newton's second law of dynamics is replaced by *F* = *ma*^{2}/*a*_{0}.

* __History__: 1983, Proposed
by Milgrom as a way to explain flat galactic rotation curves without
the need for dark matter; To explain the flatness of the curves, one can set
*a*_{0} ~ 1.2 × 10^{–10} m/s^{2} *~ cH*_{0}/6;
The effective gravitational attraction approaches (*g*_{N} *a*_{0})^{1/2},
where *g*_{N} is the usual Newtonian
acceleration; The effective force goes like 1/*r* at large distances.

* __Consequences__: When *a* =
(*g*_{N}* a*_{0})^{1/2} ("deep
MOND"), a body gravitationally bound to a mass *M* will orbit with
speed *v*^{4}
= *a*_{0}*GM*, independent of
distance! (The exponent agrees with the Tully-Fisher relation); If used as alternative
to dark matter (but possibly with a cosmological constant), the theory predicts
the ratio between the heights of the peaks of the cmb power spectrum; 2004,
*A*_{1}/*A*_{2} agrees
with WMAP data, *A*_{2}/*A*_{3}
has not been reliably measured yet.

* __Status__: 2004, It is
a phenomenological proposal, which could be related to a modification of Newton's
law of motion *F* = *ma*, or of the Poisson equation
for gravity, but is still lacking a theoretical interpretation and covariant formulation;
2004, Proposal of TeVeS by Bekenstein; 2007, University of Washington measurements support the validity of Newton's second law
down to 5 × 10^{–14} m/s^{2}.

@ __Reviews__: Milgrom APPB(01)ap-ln,
a0801-conf; Sanders MPLA(03);
Scarpa AIP(06)ap;
Frank disc(06)aug
[I]; Bekenstein CP(06)ap/07;
Milgrom a0908 [semi-popular],
AIP(10)-a0912; Dodelson IJMPD(11)-a1112-GRF, comment Moffat & Toth a1112 [challenges]; Famaey & McGaugh LRR(12)-a1112; Famaey & McGaugh a1310-conf [phenomenology]; Sanders CJP(14)-a1404 [historical perspective]; Milgrom CJP(15)-a1404; Bugg CJP(14)-a1405 [critical appraisal].

@ __General papers__: Milgrom ApJ(83), ApJ(83); Milgrom PLA(99)ap/98 [as
vacuum effect], NAR(02)ap [rev];
Sanders ap/01-conf;
Soussa & Woodard CQG(03)ap,
Soussa ht/03-proc
[non-local formulation]; Darabi IJTP(10)-a0908 [Machian
interpretation]; Milgrom MNRAS(10)-a0911
[quasi-linear formulation]; Bugg CJP(13)-a1304 [novel interpretation]; Milgrom PRD(15)-a1507 [new perspective].

@ __Relativistic__: Demir & Karahan EPJC(14)-a1408; Barrientos & Mendoza EPJP(16)-a1602.

@ __From modified inertia__: Milgrom EAS(06)ap/05-proc [modified inertia vs modified gravity]; Wang a1011; Milgrom APPB(11)-a1111-conf; Namouni MNRAS-a1504.

@ __Other origin__: Jordan ap/04 [acceleration
fluctuations]; Kao ap/06 [extra
dimension]; Blanchet CQG(07)ap/06 [gravitational
polarization]; Zaveri PiP-a0805;
Zhao a0805 [neutrino-gravity
coupling]; Milgrom ApJ(09)-a0810
[and spacetime scale invariance]; Pikhitsa a1010 [from gravitational thermodynamics]; Sebastian & Kuriakose a1104 [boundary terms in the gravitational Hamiltonian]; Bernal et al EPJC(11)-a1108, Mendoza et al AIP(12)-a1202 [MOND as weak-field limit of extended metric theories of gravity]; Bernal et al MPLA(11)-a1110 [acceleration scale as fundamental quantity]; Trippe JKAS(13)-a1303 [from massive gravitons]; Carranza & Mendoza JModP(15)-a1402 [as an entropic force]; Schiffer a1403 [cosmological expansion?]; Milgrom a1804-in [from a brane-world picture]; > s.a. entropic gravity.

@ __Other applications__: McLaughlin & Meylan ap/03-in
[MOND not needed]; Ciotti & Binney MNRAS(04)ap [two-body
relaxation].

@ __Other consequences__: Ignatiev PRL(07)gq/06 +
news pw(07)mar
[possible violation of Newton's second law – SHLEM];
Shariati & Jafari a0710 [and conservation
of energy]; Ignatiev PRD(08)-a0802 [test
using high-latitude
effect on Earth]; > s.a. black holes.

@ __Alternatives__: Romero & Zamora PRD(06)ap;
Blanchet et Combes Rech-a0910 [dipolar matter]; Rastall CJP(14)-a1401 [theory with two separate forces].

> __Online resources__: see the MOND Pages; Wikipedia page.

**And Gravitation** > s.a. MOND and astrophysics / cosmology; jacobi
dynamics; Mimetic Gravity; MOG; TeVeS; theories
of gravitation.

* __AQUAL__: An implementation
of MOND as a non-relativistic modified-gravity theory.

* __External field effect__: In
MOND, the internal dynamics of a gravitating system *s* embedded in a larger one
*S* is affected by the external background field of *S* even if it is
constant and uniform, thus implying a violation of the Strong Equivalence Principle.

@ __General references__: Mendes & Opher PLB(01)ap [sub-mm
tests]; Roscoe GRG(04);
Bekenstein PRD(04)ap;
Sanders LNP(07)ap/06;
Bruneton & Esposito-Farèse PRD(07)-a0705;
Bekenstein NPA(09)-a0901 [rev,
AQUAL], in(10)-a1001 [rev];
Zhao et al PRD(10)-a1007; Skordis & Zlosnik PRD(12)-a1101 [geometry]; Fazy PRD(13)-a1302 [MOND as quantum-statistical modified entropic gravity]; Smolin a1704 [as a regime of quantum gravity].

@ __Bimetric MOND gravity__: Milgrom PRD(09)-a0912;
Milgrom MNRAS(10)-a1001
[and twin matter]; Clifton & Zlosnik PRD(10)-a1002 [FLRW
cosmology]; Milgrom PRD(10)-a1006 [growth
of perturbations]; Milgrom PRD(14)-a1308 [gravitational waves]; Milgrom a1310-conf [rev].

@ __Other theories__: Kao gq/05 [and
induced gravity]; Zlosnik et al PRD(06)gq [vector-tensor theory];
Falcon a1007 [and FLRW cosmology];
Woodard CJP(14)-a1403 [MOND as non-local residual effect from the vacuum polarization of infrared gravitons]; Barrientos & Mendoza EPJP(17)-a1612 [as the weak-field limit of a theory with torsion]; > s.a. hořava gravity.

@ __Solutions, special systems__: Giannios PRD(05)
[spherical static solutions]; Malekjani et al ApJ(09)-a0811 [spherical collapse].

@ __Proposed tests__: Gundlach et al PRL(07)
+ pw(07)apr
[lab test]; De Lorenci et al A&A(09)-a1002 [small-acceleration
test]; Trenkel et al a1001 [LISA]; Magueijo & Mozaffari PRD(12)-a1107 [LISA Pathfinder]; Das & Patitsas PRD(13)-a1305 [in freely-falling laboratories]; > s.a. equivalence principle.

@ __Other phenomenology__:
Zhao & Famaey PRD(10) [virial theorem and elliptical shells];
Milgrom PRL(11) [and gravitational Cerenkov losses];
Milgrom MNRAS(12)-a1205 [in isolated high-acceleration systems];
Golovnev & Masalaeva GRG(14)-a1306 [gravitational collapse];
Milgrom PRD(14)-a1311 [virial theorem in general theories];
Blanchet & Bernard IJMPcs(14)-a1403 [and gravitational polarization]; Chesler & Loeb PRL(17)-a1704 [fatal inconsistencies of two relativistic generalizations with gravitational-wave observations].

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