Quasi-linear formulation of MOND

@article{Milgrom2009QuasilinearFO,
  title={Quasi-linear formulation of MOND},
  author={Mordehai Milgrom},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2009},
  volume={403},
  pages={886-895}
}
  • M. Milgrom
  • Published 2009
  • Physics
  • Monthly Notices of the Royal Astronomical Society
A new formulation of modified Newtonian dynamics (MOND) as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential φ produced by a mass distribution ρ is a solution of the Poisson equation for the modified source density ˆ ρ =− (4πG) −1 ∇· g, where g = ν(|g N |/a0)g N , and g N is the Newtonian acceleration field of ρ. This makes φ simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear… Expand
On the problem of deformed spherical systems in Modified Newtonian Dynamics
Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which theyExpand
Alternative approach to gravity and MOND
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, theExpand
Alternative approach to gravity and MOND
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, theExpand
Non-linear energy conservation theorem in the framework of special relativity
In this work we revisit the study of the gravitational interaction in the context of the special theory of relativity. It is found that, as long as the equivalence principle is respected, aExpand
Separable triaxial potential–density pairs in modified Newtonian dynamics
We study mass models that correspond to modified Newtonian dynamics (MOND) (triaxial) potentials for which the Hamilton–Jacobi equation separates in ellipsoidal coordinates. The problem is firstExpand
On the gravitational potential of modified Newtonian dynamics
The mathematical structure of the Poisson equation of Modified Newtonian Dynamics (MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev space whose Orlicz function is relatedExpand
Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments
Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of Modified Newtonian Dynamics (MOND). MOND corrections were applied to theExpand
A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales
In the pursuit of a general formulation for a modified gravitational theory at the non-relativistic level and as an alternative to the dark matter hypothesis, we construct a model valid over a wideExpand
The radial acceleration relation and a magnetostatic analogy in quasilinear MOND
Recently a remarkable relation has been demonstrated between the observed radial acceleration in disk galaxies and the acceleration predicted on the basis of baryonic matter alone. Here we study thisExpand
Studies on modified Newtonian dynamics and dark matter
STUDIES ON MODIFIED NEWTONIAN DYNAMICS AND DARK MATTER The flat rotation curves of the galaxies are considered to be anomalous observations according to Newtonian dynamics. There are two differentExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 47 REFERENCES
Vector-tensor nature of Bekenstein's relativistic theory of modified gravity
There is a distinct possibility that Newtonian gravity, and its relativistic generalization, General Relativity, breaks down in regions of small acceleration. Modified Newtonian Dynamics (MOND)Expand
Does the missing mass problem signal the breakdown of Newtonian gravity
We consider a nonrelativistic potential theory for gravity which differs from the Newtonian theory. The theory is built on the basic assumptions of the modified dynamics, which were shown earlier toExpand
Dynamics with a Nonstandard Inertia-Acceleration Relation: An Alternative to Dark Matter in Galactic Systems
Abstract We investigate particle dynamics that is governed by a nonstandard kinetic action of a special form. We are guided by a phenomenological scheme-the modified dynamics (MOND)-that imputes theExpand
Two-body relaxation in modified Newtonian dynamics
A naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t 2b implies that t 2b is comparable to the crossing time regardless of the numberExpand
The Mond Limit from Spacetime Scale Invariance
The modified Newtonian dynamics (MOND) limit is shown to follow from a requirement of spacetime scale invariance of the equations of motion for nonrelativistic, purely gravitational systems, i.e.,Expand
Relativistic gravitation theory for the MOND paradigm
The modified newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays aExpand
A stratified framework for scalar-tensor theories of modified dynamics
Although the modified Newtonian dynamics (MOND) proposed by Milgrom successfully accounts for the systematics of galaxy rotation curves and cluster dynamics without invoking dark matter, the ideaExpand
Limited utility of Birkhoff’s theorem in modified Newtonian dynamics: Nonzero accelerations inside a shell
We investigate the consequences of Birkhoff's theorem in general relativity (GR) and in modified Newtonian dynamics (MOND). We study, in particular, the system of a finite-mass test particle inside aExpand
Cosmological structure formation under MOND: a new numerical solver for Poisson's equation
We present a novel solver for an analogue to Poisson's equation in the framework of modified Newtonian dynamics (MOND). This equation is highly non-linear and hence standard codes based upon treeExpand
TOPICAL REVIEW: The tensor-vector-scalar theory and its cosmology
Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate toExpand
...
1
2
3
4
5
...