Gravity, Bose-Einstein Condensates and Gross-Pitaevskii Equation

We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small-amplitude oscillation of BEC is studied by applying variational technique to reduce the Gross-Pitaevskii equation, with gravity included, to the equation of motion of a particle moving in a potential. According to our analysis, if the s-wave scattering length can be tuned to zero using Feshbach resonance for future BEC with occupation numbers as high as ≈10²⁰, there exists a critical ground state occupation number above which the BEC is unstable, provided that its constituents interact with a 1/r³ gravity at short scales.