Recently, Harko et al. (2014) derived an approximate metric of the galactic halo in the Eddington inspired Born-Infeld (EiBI) gravity. In this metric, we show that there is an upper limit ρ is a remarkable prediction of the EiBI theory.
We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko et al. (2014). It turns out that stability depends more strongly on the dark matter central density ρ 0 than on other parameters of the solution. This property then yields an upper limit on ρ 0 for each individual galaxy, which we call here ρ upper 0 , such that stable circular orbits are possible only when the constraint ρ 0 ≤ ρ upper 0 is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius R DM ∼ 180 kpc and find that ρ upper 0 ∼ 2.37 × 10 11 M kpc −3 . This limit turns out to be about four orders of magnitude larger than the latest data on central density ρ 0 arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.
Let Ω be a multiply-connected domain in R n (n ≥ 2) of the form Ω = Ωout \Ωin. Set ΩD to be either Ωout or Ωin. For p ∈ (1, ∞), and q ∈ [1, p], let τ1,q(Ω) be the first eigenvalue ofUnder the assumption that ΩD is convex, we establish the following reverse Faber-Krahn inequality τ1,q(Ω) ≤ τ1,q(Ω ⋆ ), where Ω ⋆ = BR \Br is a concentric annular region in R n having the same Lebesgue measure as Ω and such that (i) (when ΩD = Ωout) W1(ΩD) = ωnR n−1 , and (Ω ⋆ )D = BR, (ii) (when ΩD = Ωin) Wn−1(ΩD) = ωnr, and (Ω ⋆ )D = Br. Here Wi(ΩD) is the i th quermassintegral of ΩD. We also establish Sz. Nagy's type inequalities for parallel sets of a convex domain in R n (n ≥ 3) for our proof.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.