Modifications
of Newtonian Gravity| Modifications
of Newtonian Gravity |
In General > s.a. [newtonian gravitation];
covariant quantum gravity; graviton.
* Motivation: Originally
(1905) the realization that Newtonian gravitation was incompatible with special
relativity; Poincaré made the first attempt to modify the theory; 2001,
Interest has increased recently because of proposed higher-dimensional models
with
4D spacetime as brane, and to some extent because of
possible
alternative to dark matter in explanations of galactic dynamics.
* Radial dependence:
The only corrections to the potential consistent
with relativistic field theory are Yukawa-type,
U(r) = –G mm'/r – 
G (mm'/r)
exp{–r/
}
,
where the range is
related to the graviton mass by mg =
/c.
@ General articles: Shelupsky AJP(85)dec
[and light bending]; Cook CP(87);
Milgrom Rech(88)feb; Parker & Zumberge Nat(89)nov;
Onofrio MPLA(98)
[motivation and tests]; Mostepanenko gq/03-in
[Casimir force].
@ Early work on non-Newtonian effects: Heaviside 1894 [gravitomagnetism];
Forward PIRE(61).
@ Phenomenology: Marinoni & Piazza ap/03/ApJL
[GraS]; Dvali ht/04-in
[infrared]; > s.a. MOND.
> Phenomenology: see
orbits in newtonian gravity; phenomenology
of gravity; Sagnac
Effect; tests of general relativity; tests
of newtonian gravity.
Sources of Corrections > s.a. brane
phenomenology; fifth
force; higher-dimensional gravity; quantum-gravity
effects.
@ General relativistic: Iorio GJI(06)gq [on
Earth, and possible measurement].
@ Quantum: Donoghue PRL(94);
Kazakov CQG(01);
Kirilin & Khriplovich JETP(02)gq;
Kirillov & Turaev G&C(03)ht/01 [spacetime
foam]; Ward IJMPA(05)
[resummed quantum gravity]; Bailey & Kostelecky PRD(06)gq
[with Lorentz symmetry violation]; Akhundov & Shiekh EJTP(08)-gq/06 [rev];
Faller PRD(08)-a0708 [from
effective quantum gravity and scalar QED]; Caldwell & Grin PRL(08)
[modifications below 0.05 mm and cosmology].
@ From string theory: Antoniadis hp/99-in;
> s.a. string
phenomenology.
Parametrized Post-Newtonian (PPN) Formalism > s.a. phenomenology;
self-force; tests
of general relativity.
* Idea: A framework for
comparing general relativity with other metric theories, using 10 parameters
which can be experimentally determined; It includes the PN approximation
of (nearly) every metric theory, but only treats conservative aspects
and does not include radiation.
* Interpretation: For an isolated, spherical object, if 
represents
the non-linearity in gravitational attraction, and 
the amount of curvature
produced by a body,
g00 = –1 +
2U , gij
= (1 + 2 M/R) 
ij
+ ... , where U = M/R – (M/R)2 +
...
* Parameter values:
2004, From Cassini data, –1
= (1.2 
1.1) ×
10–4; 2006, Bounds on and are
10–4–10–5,
various missions to improving limits by several orders of magnitude
(LATOR, ASTROD, BepiColombo, GAIA) under consideration; 2006, on galactic scales,
= 0.98 0.07
(68% cl).
@ General references: in Eddington 22; Robertson in(62); Schiff SIAM(62),
in(67); Nordtvedt PR(68), PR(68),
PR(69);
Will ApJ(71); Will & Nordtvedt
ApJ(72); in Misner et al 73, Ch39; Rendall
PRS(92);
Kopeikin & Vlasov PRP(04)
[reference frames, scalar-tensor theory]; Blanchet et al PRD(05)gq
[structure, near zone]; Allemandi et al GRG(05)gq [alternative
theories].
@ Values: Arminjon gq/03-in
[new method]; Bolton et al PRD(06)ap [ on
galactic scales]; Alexander & Yunes PRD(07),
PRL(07)ht [for Chern-Simons gravity].
@ Effects: Rama & Ghosh PLB(96),
same as PLB(96)
[values for repulsive gravity]; Schröder & Treder
FP(02)
[Earth-Moon system]; Arminjon PRD(05)gq,
gq/05-in [corrections
to equations of motion and new self-acceleration].
@ Variations: Xu & Ma PLB(07)
[for 5D gravity, and tests of Kaluza-Klein theory]; Clifton PRD(08)-a0801 [for
fourth-order theories].
> Related topics:
see cosmological models [post-Friedmann framework];
lorentz-symmetry phenomenology; motion
of
test
particles and gravitating
bodies; sources of gravitational waves; higher-order
theories [Newtonian
limit]; dark
matter; newton-cartan
theory.
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send feedback and suggestions to bombelli at olemiss.edu – modified 14
aug 2009