Modified Newtonian Dynamics (MOND)| Modified Newtonian Dynamics (MOND) |
In General > s.a. variation of constants.
* Idea: At accelerations below
a certain value a0 (g
= ∇Φ < a0),
Newton's second law of dynamics is replaced by F
= ma2/a0.
* 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
a0 ~ 1.2 × 10−10
m/s2 ~ cH0/6;
The effective gravitational attraction approaches (gN
a0)1/2,
where gN is the usual Newtonian
acceleration; The effective force goes like 1/r at large distances.
* Consequences: When a
= (gN
a0)1/2
("deep MOND"), a body gravitationally bound to a mass M
will orbit with speed v4
= a0GM, 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,
A1 / A2
agrees with WMAP data, A2
/ A3 has not been reliably measured yet.
* Status: 2004, It is a
phenomenological proposal, possibly 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/s2; 2018, More lack of evidence of a fundamental
acceleration in galaxies.
@ 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];
Sanders 16 [and concordance cosmology];
Merritt 20 [philosophical].
@ 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],
SHPMP(20)-a1910-conf [vs dark matter].
@ Relativistic: Demir & Karahan EPJC(14)-a1408;
Barrientos & Mendoza EPJP(16)-a1602;
Sussman & Hernández a1908 [and cosmic expansion rate].
@ From modified inertia: Milgrom EAS(06)ap/05-proc [modified inertia vs modified gravity];
Wang a1011;
Milgrom APPB(11)-a1111-conf;
Namouni MNRAS-a1504;
Costa et al a1904 [local Lagrangian].
@ As weak-field limit of extended metric theories:
Bernal et al EPJC(11)-a1108,
Mendoza et al AIP(12)-a1202;
Barrientos & Mendoza PRD(18)-a1808.
@ 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 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];
Giusti a2002,
Varieschi a2003 [based on fractional calculus formalism];
> 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 PRD(17)-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];
Christodoulou & Kazanas a1901 [as low-acceleration limit of G(a) gravity];
Skordis & Złosnik a2007;
Barrientos et al a2008 [with curvature-matter couplings];
> 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];
Klein CQG(20)-a1901 [evidence from Cavendish-type experiments].
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