Quasi-linear formulation of MOND
By Mordehai Milgrom. 2009
190 citations recorded by the source corpus.
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-differential equations, with one non-linear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct centre-of-mass acceleration to composite bodies. The theory is akin in some respects to the non-linear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c30e810de868247ddf32488b205dd79aea3b69b
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Citations in the corpus
- The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology (2012, background): “A quasilinear formulation of Milgromian dynamics has been discovered only recently (Milgrom 2010; Zhao&Famaey 2010) which appears to allow easier access to N-body calculations.”
- One Law to Rule Them All: The Radial Acceleration Relation of Galaxies (2016, methodology): “For LTGs, ETGs, and classic dSphs, we find that the relation is consistent with a low-acceleration slope of 0.5 and α = 1 for every galaxy, in agreement with general MOND predictions.”
- Fitting the radial acceleration relation to individual SPARC galaxies (2018, unknown): “The scale invariance can be achieved in two ways: modified gravity (MG) by changing the Poisson equation (Bekenstein & Milgrom 1984; Milgrom 2010), and modified inertia (MI) by changing the Second Law of Newton (Milgrom 1994).”
- Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions (2011, background): “Another way [319] of modifying gravity in order to reproduce Milgrom’s law is to still keep the “matter action” unchanged Skin + Sin = ∫︀ ρ(v(2)/2 − Φ)d(3)x dt, thus ensuring that varying the action of a test particle with respect to the particle degrees of freedom leads to d(2)x/dt(2) = −∇Φ, but to”
- Galaxies as simple dynamical systems: observational data disfavor dark matter and stochastic star formation (2014, methodology): “14) is not unique, as yet another formulation at the classical level has recently been presented (see [11, 235] for details) and implemented in the Phantom of Ramses (POR) simulation code (Lüghausen, Famaey & Kroupa 2014, [236]).”
- Local-Group tests of dark-matter concordance cosmology - Towards a new paradigm for structure formation (2010, background): “…Blanchet & Le Tiec 2009; Esposito-Farèse 2009; Skordis 2009; Milgrom 2009b) are currently under intense scrutiny, and a qu silinear formulation of MOND has been discovered only recently (Milgrom 2010; Zhao & Famaey 2010), which appears to allow easier access to N-body calculations.”