It is not Easy to Replace Newtonian Gravitational Theory! [chapter]

D. Gerbal, H. SirousseZia
1988 Large Scale Structures of the Universe  
Paris 1-The great amount of unseen dynamical matter in large scale structures is derived from: the Newton's law of inertia and the theory of gravitation.But none of these law has been tested on scale larger than r>10Kpc.It is then tempting to modify them following: V = G-[ 1 +Σ ajexpi-)] Gibbons & Whiting, 1981; Sanders,1984 (1) Γ i r i F=mag(-) Milgrom,1983 (2) a o where g(x) is a phenomenological function. 2-We argue on both theoretical, observational and experimental grounds against the
more » ... ds against the law(l).Up to now, we consider: -a non-relativistic theory with a single potential as (1) exists only if Zaj=-1 (Gerbal &SirousseZia, 1987) which implies that there is no gravitation at small scale (for instance in the solar system!); -a (massive) Brans-Dicke-like theory: a^=l/3, r^lkm (Fujii,1971,1974), which is too small compare to r 1 «20-40Kpc needed by Sanders(1984); -a quadratic Lagrangian theory: or Xaj = -1 again (Stelle, 1978), or a false value for the light 602 /. Audouze et al. (eds.), Large Scale Structures of the Universe, 602. ©1988 by the IAU. available at https://doi.
doi:10.1007/978-94-009-2995-1_153 fatcat:ewbwqo4vcvfflklgu5c4g54lfi