Collective excitations of a "gravitationally" self-bound Bose gas

We investigate the collective excitations of an atomic Bose-Einstein conden sate in the self-binding regime produced by electromagnetically induced "gr avity" (1/r attraction). Analytical expressions for the frequencies of the monopole and quadrupole modes are obtained at zero temperature, using the s um-rule approach, and compared with the exact results available in the Thom as-Fermi limit. The low-energy dynamics of such condensates is shown to be dominated by the effective "plasma" frequency. An analog of the Jeans gravi tational instability is analyzed.