The Non-universal behaviour of Cold Fermi Condensates with Narrow Feshbach Resonances

In this paper we construct an effective field theory for a condensate of cold Fermi atoms whose scattering is controlled by a narrow Feshbach resonance. We show how, from first principles, it permits a hydrodynamic description of the BEC-BCS crossover from which the equation of state, intimately related to the speed of sound, can be derived. Specifically, we stress the non-universal behaviour of the equation of state at the unitary limit of infinite scattering length that arises when either, or both, of the range of the inter-atomic force and the scale of the molecular field become large.Comment: 7 pages, there is no differences in results between this (v2) and the older version (v1), but v2 makes the nature of the non-canonical behavior of the EOS cleare

Null and time-like geodesics in Kerr-Newman black hole exterior

We study the null and time-like geodesics of the light and the neutral particles respectively in the exterior of Kerr-Newman black holes. The geodesic equations are known to be written as a set of first-order differential equations in Mino time from which the angular and radial potentials can be defined. We classify the roots for both potentials, and mainly focus on those of the radial potential with an emphasis on the effect from the charge of the black holes. We then obtain the solutions of the trajectories in terms of the elliptical integrals and the Jacobian elliptic functions for both null and time-like geodesics, which are manifestly real functions of the Mino time that the initial conditions can be explicitly specified. We also describe the details of how to reduce those solutions into the cases of the spherical orbits. The effect of the black hole's charge decreases the radii of the spherical motion of the light and the particle for both direct and retrograde motions. In particular, we focus on the light/particle boomerang of the spherical orbits due to the frame dragging from the back hole's spin with the effect from the charge of the black hole. To sustain the change of the azimuthal angle of the light rays, say for example $\Delta \phi=\pi$ during the whole trip, the presence of the black hole's charge decreases the radius of the orbit and consequently reduces the needed values of the black hole's spin. As for the particle boomerang, the particle's inertia renders smaller change of the angle $\Delta \phi$ as compared with the light boomerang. Moreover, the black hole's charge also results in the smaller angle change $\Delta \phi$ of the particle than that in the Kerr case. The implications of the obtained results to observations are discussed.Comment: 50 pages, 18 figure