TY - JOUR

T1 - Comparing different realizations of modified Newtonian dynamics

T2 - Virial theorem and elliptical shells

AU - Zhao, Hongsheng

AU - Famaey, Benoit

PY - 2010/4/20

Y1 - 2010/4/20

N2 - There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula, modified Newtonian dynamics (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (bimetric MOND, leading for a given set of parameters to the quasilinear MOND, and Bekenstein's Tensor-Vector-Scalar). In this limit, these theories are constructed to give the same force field for spherical symmetry, but their predictions generally differ out of it. However, for certain realizations of these theories (characterized by specific choices for their free functions), the binding potential-energy of a system is increased, compared to its Newtonian counterpart, by a constant amount independent of the shape and size of the system. In that case, the virial theorem is exactly the same in these two theories, for the whole gravity regime and even outside of spherical symmetry, although the exact force fields are different. We explicitly show this for the force field generated by the two theories inside an elliptical shell. For more general free functions, the virial theorems are, however, not identical in these two theories. We finally explore the consequences of these analytical results for the two-body force.

AB - There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula, modified Newtonian dynamics (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (bimetric MOND, leading for a given set of parameters to the quasilinear MOND, and Bekenstein's Tensor-Vector-Scalar). In this limit, these theories are constructed to give the same force field for spherical symmetry, but their predictions generally differ out of it. However, for certain realizations of these theories (characterized by specific choices for their free functions), the binding potential-energy of a system is increased, compared to its Newtonian counterpart, by a constant amount independent of the shape and size of the system. In that case, the virial theorem is exactly the same in these two theories, for the whole gravity regime and even outside of spherical symmetry, although the exact force fields are different. We explicitly show this for the force field generated by the two theories inside an elliptical shell. For more general free functions, the virial theorems are, however, not identical in these two theories. We finally explore the consequences of these analytical results for the two-body force.

UR - http://www.scopus.com/inward/record.url?scp=77952989812&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.81.087304

DO - 10.1103/PhysRevD.81.087304

M3 - Article

AN - SCOPUS:77952989812

SN - 1550-7998

VL - 81

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 8

M1 - 087304

ER -