Modified Newtonian dynamics habitats within the solar system

Abstract

MOdified Newtonian Dynamics (MOND) is an interesting alternative to the presence of dark matter in galaxies. We here examine the possibility that mild or even strong MOND behavior may become evident well inside the solar system, in particular, near saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizable oblate ellipsoid around the saddle point. We work out the MOND effects using the nonrelativistic limit of the $\mathrm{T}e\mathrm{V}e\mathrm{S}$ theory, both in the perturbative nearly Newtonian regime and in the deep MOND regime. While strong MOND behavior would be a spectacular ``backyard'' vindication of the theory, pinpointing the MOND bubbles in the setting of the realistic solar system may be difficult. Space missions, such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region.