Gravity with Extra Dimensions and Dark Matter Interpretation: A Straightforward Approach
Figure 1
(a) The rotation curves of an effective potential where the Poisson equation is solved from a Miyamoto-Nagai ansatz, with parameters and , describing a disk galaxy and where the Laplace equation for the extra field is solved by a Chazy-Curzon disk, with stable cut parameter . They correspond to gravitating particles which orbit in a background. The full line is the curve when there are no extra dimensions; that is, . The dotted lines represent a set of extra dimensional solutions for fixed and varying from to , as in [19]. The parameters , , and are chosen in order to make the orbital motion stable. (b) The same set of solutions presented in (a), but now we represent the squared epicyclic frequency . When this last is positive, we guarantee the stability of the system.
